The following is the in-game prologue from the SNES version of the game:

Long ago, in the beautiful kingdom of Hyrule surrounded by mountains and forests... legends told of an omnipotent and omniscient Golden Power that resided in a hidden land.
Many people aggressively sought to enter the hidden Golden Land... But no one ever returned.
One day evil power began to flow from the Golden Land... So the King commanded seven wise men to seal the gate to the Land of the Golden Power. That seal should have remained for all time...
...But, when these events were obscured by the mists of time and became legend...
A mysterious wizard known as Agahnim came to Hyrule to release the seal. He eliminated the good King of Hyrule...
Through evil magic, he began to make descendants of the seven wise men vanish, one after another.
And the time of destiny for Princess Zelda is drawing near.

Backstory

This is the backstory and prologue from the booklet for the SNES version of A Link to the Past, starting at page 3, and ending at page 8:

To set the stage for this adventure of the legendary Hero of Hyrule, it will be informative to delve into the Triforce myth, an ancient epic about the creation of the world that is still believed in the land of Hyrule. Every culture has such myths and theories about the creation of their worlds, and it can be beneficial and entertaining to examine them in detail, for they often affect the present day social structure. The legends say the mythical gods of Hyrule had as their chosen people the Hylia[ns]. These ancient people left scrolls that are the primary source of the legends.

According to the Hylian scrolls, the mythical gods descended from a distant nebula to the world and created order and life. The God of Power dyed the mountains red with fire and created land. The God of Wisdom created science and wizardry and brought order to nature. And the God of Courage, through justice and vigor, created life- the animals that crawl the land and the birds that soar in the sky. After the gods had finished their work, they left the world, but not before creating a symbol of their strength, a golden triangle known as the Triforce. A small but powerful portion of the essence of the gods was held in this mighty artifact, which was to guide the intelligent life on the world of Hyrule.

Although it was an inanimate object, the Triforce had the power to bestow three titles which gave the person who received them great powers: "The Forger of Strength", "The Keeper of Knowledge", and "The Juror of Courage". From its hiding place in the so-called Golden Land where the Gods placed it, the Triforce beckoned people from the outside world to seek it in the hope that someone worthy of these titles would find it. With their magic infused blood, the Hylian people were endowed with psychic powers and skill in wizardry. It was also said that their long, pointed ears enabled them to hear special messages from the gods, so they were held in high esteem by many people in Hyrule. Their descendants settled in various parts of the world and passed on their knowledge and magical lore to all people. But in its passing, the lore was often distorted or lost altogether.

In Hyrule, there are many Hylian buildings which are mentioned repeatedly in the legends. These buildings, which now lie in ruin, pale shadows of their former splendor, are closely tied to the Triforce. Some were even said to house the Triforce...

If it were only a symbol of the gods, the Triforce would be coveted by many. But a verse from the Book of Mudora (a collection of Hylian legends and lore) made the Triforce even more desirable:

"In a realm beyond sight,
The sky shines gold, not blue.
There, the Triforce's might
Makes mortal dreams come true."

Many aggressively searched for the wish-granting Triforce, but no one, not even the Hylian sages, was sure of its location; the knowledge had been lost over time. Some said the Triforce lay under the desert, others said it was in the cemetery in the shadow of Death Mountain, but no one ever found it. That yearning for the Triforce soon turned to lust for power, which in turn led to the spilling of blood. Soon, the only motive left among those searching for the Triforce was pure greed.

One day, quite by accident, a gate to the Golden Land of the Triforce was opened by a gang of thieves skilled in the black arts. This land was like no other. In the gathering twilight, the Triforce shone from its resting place high above the world. In a long running battle, the leader of the thieves fought his way past his followers in a lust for the Golden Power. After vanquishing his own followers, the leader stood triumphant over the Triforce and grasped it with his blood-stained hands. He heard a whispered voice: "If thou has a strong desire or dream, wish for it..." And in reply, the roaring laughter of the brigand leader echoed across time and space and even reached the far-off land of Hyrule. The name of this king of thieves is Ganondorf Dragmire, but he is known by his alias, Mandrag Ganon, which means "Ganon of the Enchanted Thieves".

I do not know what Ganon wished for from the Triforce. However, in time evil power began to flow from the Golden Land and greedy men were drawn there to become members of Ganon's army. Black clouds permanently darkened the sky, and many disasters beset Hyrule. The lord of Hyrule sent for the Seven Wise Men and the Knights Of Hyrule, and ordered them to seal the entrance to the Golden Land.

The Triforce, being an inanimate object, cannot judge between good and evil. Therefore, it could not know that Ganon's wishes were evil; it merely granted them. Suspecting that Ganon's power was based on the Triforce's magic, the people of Hyrule forged a sword resistant to magic which could repulse even powers granted by the Triforce. This mighty weapon became known as the blade of evil's bane, or the Master Sword. It was so powerful that only one who was pure of heart and strong of body and mind could wield it. As the Seven Wise Men searched for a valiant person to take up the Master Sword, Ganon's evil army swarmed from the tainted Golden Land into Hyrule and attacked the castle. The wise men and the Knights Of Hyrule combined forces to wage war on this evil horde.

The Knights took the full brunt of the fierce attack, and although they fought courageously many a brave soul was lost that day. However, their lives were not lost in vain, for they bought precious time for the Seven Wise Men to magically seal Ganon in the Golden Land. All of Hyrule rejoiced at the victory that upheld peace and order over Ganon's evil and chaos. This war, which had claimed many lives, became known as the Imprisoning War in stories told in later centuries.

Many centuries have passed since the Imprisoning War. The land of Hyrule healed its wounds and the people lived in peace for a long time. Memories of the vicious Imprisoning War faded over the generations...

So it is no surprise that no one was prepared for the new disasters that have recently struck Hyrule. Pestilence and drought, uncontrollable even by magic, ravaged the land. The King of Hyrule, after counsel with his sages, ordered an investigation of the Imprisoned Dark World (as the Golden Land had come to be known) but the wise men's seal was apparently intact. He offered rewards for anyone who could find the source of these troubles. In answer to these summons, a stranger named Agahnim came and quelled the disasters with a previously unseen form of magic. As a reward, the king gave him a new position as chief advisor and heir to the Seven Wise Men. The masses proclaimed him their hero. Peace had returned to Hyrule... or had it?

Of late, rumors have traveled their whispering path with alarming frequency. Rumors saying Agahnim now rules the country with his magic... Rumors of strange magical experiments in the castle tower at night... The people of Hyrule were gripped by dread.

Prologue

One night, a girl's voice awakens you from your sleep.
She telepathically pleads.

"Help me...
My name is Zelda...
I am in the castle dungeon."

You jump out of bed not knowing whether the voice was part of a dream or reality. Upon leaving your bed, you find your uncle, who should be fast asleep at this time, preparing to go out, girded for battle.
"I'll be back by morning," he says as he departs. "Don't leave the house."
You watch him leave with the family sword in hand and shield on arm. This night is like no other... Who is Zelda? Where had your uncle gone and for what reason?
And so, on an ill-fated night, a new chapter in the legend of Hyrule's hero begins- a new chapter in The Legend of Zelda!

The following is the in-game prologue from the GBA version of the game:

Long ago, in Hyrule, a beautiful kingdom surrounded by forests and mountains... legends told of an omnipotent and omniscient Golden Power that lay hidden.
It was hidden in a sacred realm beyond the reach of men, but one day... a doorway to that realm was suddenly opened...
Hoping to claim the Golden Power as their own, the people began to quarrel and fight... Many sought to enter the hidden Golden Land... But none returned, and instead evil power began to issue forth from the dark portal... So the king commanded seven sages to seal the gate to the land of the Golden Power.
Many brave knights were lost in the battle to protect the sages from the tides of evil, but the seal was cast! Evil flowed no more! And the seal would remain for all time... Or so the people hoped...
But when these events were obscured by the mists of time, and became legend...
A mysterious wizard known as Agahnim appeared as from nowhere... and with strange magic powers he eliminated the good king of Hyrule...
He cast spells on the soldiers and kidnapped young maidens descended from the sages in order to break the seal...
This destiny fast approaches for the final maiden... the princess, Zelda...

Backstory

This is the backstory given in the booklet for the GBA port of A Link to the Past. In this version, the backstory was shortened and changed from the original version in the SNES. The prologue goes from page 14 to 15.

Aeons ago, the Deities of Power, Courage, and Wisdom descended to the world of chaos. They created the world that we know and left behind a symbol of their strength- the golden emblem known as the Triforce, which they hid in the Golden Land.

After many years, an opening was found that led from our fair Hyrule to the Golden Land, where the mystical Triforce was still hidden. Many sought the treasure in this place, but none returned- only beings of great evil emerged from the Golden Land.

The King of Hyrule gathered the Seven Sages to find a way to seal the entrance to the Golden Land, so that his kingdom would be safe from the evil there. The Sages succeeded and brought peace again to Hyrule.

However, strange things have been happening in Hyrule since the appearance of Agahnim, a mysterious sorcerer who gained fame for extinguishing a devastating blaze of unknown origin some years ago.

And now...

One night, a girl's voice wakes you from your sleep. "Help me... my name is Zelda... I am in the castle dungeon." Not knowing if the voice was a dream or reality, you step into the rain and forbidding darkness...and the Legend of Zelda begins.

Lastly, the following is the explaination of the events leading to A Link to the Past, as told in the Hyrule Historia.

Ganondorf the thief obtained the Triforce of Power and managed to get his hands on Princess Zelda. The Hero of Time, Link, challenged him in a battle that would determined Hyrule's very existence, and lost.

At last, Ganondorf found himself in the possession of the Triforce of Wisdom that dwelt within Princess Zelda, and the Triforce of Courage that dwelt within Link. His true power achieved, he transformed into the Demon King. The Seven Sages of Hyrule, led by Princess Zelda, sealed Ganon and the Triforce in the Sacred Realm as a final resort.

For a brief time, it seemed as though peace had returned to the kingdom.

However, there were many who knew of the existence of the Triforce and the entrance to the Sacred Realm because of the events set in motion by Ganondorf. Their lust aroused, they rushed to gain access to the holy land in the quest to obtain the power of the gods.

Little did they realize that the Sacred Realm had been transformed into the Dark World by Ganondorf's evil heart. None returned from their adventures. Instead, only the power of darkness flowed forth.

The king of Hyrule ordered the Seven Sages to seal the Sacred Realm. The Knights of Hyrule guarded the sages as they offered up their prayers, but demons descended upon them from within the Sacred Realm, and a fierce battle unfolded in which the majority of the combatants were killed.

The entrance to the Sacred Realm was sealed once again, tight enough that it should never have been reopened.

Until the era of the Hero of Time, the kingdom of Hyrule was mostly inhabited by the Hylian people, whose existence was linked to their goddess, Hylia. Hylians possessed a special power: it was said that their long ears allowed them to hear the voices of the gods.

However, the kingdom fell into ruin during the Imprisoning War, and the bloodline of the Hylians weakened with the ages, until their existence was naught but a thing of the past. The sages' power also waned, and Hyrule, once called the Kingdom of the Gods, became nothing more than an ancient legend.

Though the power of the Triforce and the blood of the Hylians continued to wane, Hyrule remained at peace. That is, until the appearance of a man who sought to break the seal on the Sacred Realm, which had been transformed into the Dark World. He was a priest who went by the name of Agahnim, and he wielded powerful magic.

Agahnim sent the king to an early grave. Putting the soldiers of the kingdom under his spell, he kidnapped the maidens in whose veins flowed the blood of the Seven Sages. One by one, he sacrificed the girls, sending them to the Dark World, and was about to offer up Princess Zelda as well.

When talking about the story of A Link to the Past it's important to remember that this was the first Zelda that had a story that went beyond a single paragraph. Not only did the writters not have any idea of a timeline yet, but they also didn't even know which elements would stuck and which would be retconed in later games.
Reading through the original backstory there are a lot of parts where I'm surprised by how little has changed when it comes to other games. For example, the origin of the Triforce story is basically the exact same as how it appeared in Ocarina of Time, other than that fact that the "gods" where changed to "goddesses". However, there are still several parts that I want to note, either because they are later retconned, or are just interesting. It have listed them here:

The word "Hylia" is used interchangably with "Hylians". This is pretty confusing from the perspective of a modern Zelda fan.

The titles of "The Forger of Strength", "The Keeper of Knowledge", and "The Juror of Courage" are very interesting, though they are never mentioned again in the series.

The sentence "...so [the Hylians] were held in high esteem by many people in Hyrule." seemed to imply that the Hylians are/were a minority group, seperate from most of the main population in Hyrule.

This is the first time Ganondorf (not Ganon) was mentioned in the series. For a long time I always assumed that the name Ganondorf was something Ocarina of Time invented.

Ganondorf also has a last name here. "Ganondorf Dragmire" which is never mentioned in any other games.

Interestingly, the backstory is told in first person. There sentence "I do not know what Ganon wished for from the Triforce." seems to suggest that someone is telling this story, though it's unclear who. (I don't actually own an ALTTP manual so it might be made more clear somewhere else in the manual, but I'm not aware of this.) Interestingly, the GBA version has a similar case of first-person pronouns in the sentence "...an opening was found that led from our fair Hyrule to the Golden Land..."

The Hylians are said to have made the master sword for the imprisoning war. This would've made sense at the time, since this is the first game where the master sword appears, however it was retconned since it doesn't really fit in the context of every other game.

I feel as though the GBA version was aware of how the story of ALTTP clashed with the story of every other Zelda game, but instead of seriously retconning it, they just made the story as vague as possible. The backstory section is drastically shortened and doesn't go into nearly as much detail. They even avoided saying the three "goddesses", instead using the word "deities", even though as this point the three goddesses were well established in Zelda canon.
Considering all the retcons and what not going on here, I feel like the Imprisoning War is least understood part of the Zelda timeline. I personally think the Hyrule Historia version of events is best, since, unlike the GBA version, it goes into a far amount of detail, and unlike the SNES version it doesn't directly conflict with later games. But I still wanted to briefly give my own take on the story:

After the events of Ocarina of Time we follow the downfall timeline. Link is defeated in the battle with Ganondorf, giving him access to the full Triforce. In an attempt to try and stop him Zelda and the sages seal him in the Sacred Realm. The Sacred Realm transforms into the dark world- a twisted version of Hyrule for him to rule over.
The people of Hyrule were aware of the Triforce and now knew that it was sealed in the Sacred Realm. Many people, fueled by greed, attempted to find an enterance to the Sacred Realm, but once they got there they found they couldn't leave and unintentionally became part of Ganon's growing army.
As a result of many people finding ways into the Sacred Realm the seal began to grow weak. It became weak enough that Ganon was able to lead his army into Hyrule, resulting in the Imprisoning War. Most of the soldiers of Hyrule were killed as they bought time for the seven wise men/sages to reseal the Sacred Realm. (These are either the same sages from Ocarina of Time, or their descendants, it doesn't really matter.) They managed to reseal Ganon in the Sacred Realm, this time permanently, they thought.
After seeing the Imprisoning War few people tried to seek out the Triforce anymore, and over time the knowledge of Triforce faded. The Hylians slowly lost their connection to the goddesses and to magic.
Many centuries later, the seven maidens (descendants of the seven sage) have magic that is much weaker than sages, but is still present enough that their existence allows the seal on the Sacred Realm to remain.
In that time Hyrule was in an age of peace, until several natural disasters came across Hyrule. The king was approached by Agahnim, a mysterious sorcerer who was able to stop these disasters using powerful magic. (Though actually it was Agahnim who caused them in the first place.) After that he became an advisor to the king, an we all know how that turns out...

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