Setting the foundation of the Zelda timeline before A Link Between Worlds was placed on it.
Before we take a closer look at where A Link Between Worlds sits on the Nintendo Timeline, I think it’s important to have a solid understanding of the back-story of the games on this branch of the Zelda mythos. So get ready to read a shortened version of the Zelda story as Nintendo tells it in their epic book, Hyrule Historia.
(Note: In order to keep things as brief as possible I will only focus on the branch relevant to A Link Between Worlds.)

Nintendo Timeline (Before ALBW Placement):
At the end of Ocarina of Time, Link faces Ganondorf and is defeated. Ganondorf then obtains the full Triforce, turning him into Ganon, and threatened Hyrule for a while. Eventually, Zelda and the seven Sages are successful in sealing Ganon and the Triforce into the Sacred Realm.
After these events the Imprisoning War took place. Many people tried to get into the Sacred Realm to find the Triforce, but they never made it back since Ganon had turned it into the Dark World. In order to keep people safe, the seven Sages sealed the Sacred Realm shut.
The events of A Link to the Past then take place. Ganon, through the use of Agahnim in Hyrule, captures the descendants of the seven Sages, and Princess Zelda, in order to break the seal on the Sacred Realm so he may escape and rule Hyrule as well. In order to prevent Ganon from escaping, and thus destroying the Light Realm, Link rescued the Sages and Zelda. Link then broke into Ganon’s pyramid in the Sacred Realm and destroyed the beast in battle. In the end Link used the Triforce to wish those affected by Ganon’s reign of terror back from the dead. The Triforce then rested in the hands of Hyrule’s royal family.

Next up the events of the Oracle games occur. In short, Kotake and Koume (Twinrova) attempted to resurrect the dead Ganon by performing a ceremony. The twin witches were nearly successful and were able to perform part of the resurrection ceremony. However, since the ritual wasn’t fully completed, Ganon was only resurrected as a “witless” beast that Link defeated.
Link’s Awakening then takes place, but the events of this game are largely irrelevant due to the majority of the story being a dream.
We then enter the “Golden Era” of the timeline. A King of Hyrule used the Triforce for good, but he was worried about how the artifact would be used after his death. In order to prevent abuse the King placed a spell over Hyrule and hid the Triforce. It is said that the Triforce would then appear on the back of the hand of a person worthy of wielding it.
This King did this because he didn’t believe his son, heir to the throne, would use the Triforce properly. However, the King secretly passed on a piece of the Triforce to his daughter, Princess Zelda.

The “Era of Decline” then takes place. The old King dies and his son takes over. The new King is angry about not having the Triforce and knows Zelda is hiding details. A powerful Wizard, who is the King’s advisor, then threatens to put Zelda in an eternal sleep if she doesn’t talk. Zelda refuses and she is then sent into a deep slumber.
Zelda’s brother, the King, is then very sorrowful about what has happened. Zelda is then placed upon an alter and rests there until they can find a solution. Every princess from that day onward is then named Zelda so the people never forget this tragedy.
The Legend of Zelda, and The Adventures of Link take place after this. However, their story is not needed to prove any points in the sake of the A Link Between Worlds discussion.