The story of Ocarina of Time takes place longer ago than you may imagine. It is actually a prequel to The Legend of Zelda: A Link to the Past. To understand where the game starts, you have to go back to creation of the world.
The world was born when three goddesses, Din, Nayru, and Farore created it, each creating a different aspect of it. Din, the goddess of power, created the earth and land, and gave it form. Nayru, the goddess of wisdom, gave the spirit of law to the world. Farore, the goddess of courage, created all life forms to uphold the law. Upon leaving, the goddesses created the Triforce, a symbol of high respect which is in the shape of three golden triangles together as one, on the spot where they left this earth. The Triforce holds much power, and will grant the single wish of the one who possesses it. It became the most holy and worshipped symbol in the world, and the people decided to build their towns around it. It remains in Hyrule, a peaceful town ruled by the king and his daughter, Princess Zelda. More specifically, it is in the Sacred Realm, the entrance to which is in the Temple of Time, and can only be reached by a chosen hero along with the Ocarina of Time and the three Spiritual Stones.
In the Kokiri Forest, a forest near the middle of Hyrule, everyone has a guardian fairy - everyone except for a young boy named Link. Every night, he has the same nightmare. In this nightmare, he is standing outside the moat leading to the castle, while the drawbridge is opening, and a thunderstorm is raging. He sees two women, one older, one younger and more beautiful fleeing on a white horse. After watching them for a few seconds, he turns around only to be face-to-face with a vicious-looking man on a black horse.
Link is woken up by a fairy named Navi. He finds out that Navi was sent by the Great Deku Tree, the guardian spirit of the Kokiri Forest, to summon him. They travel together to see the Deku Tree, where Link is told that the Deku Tree has a curse on it, and only he can break it. The giant tree opens his mouth, revealing a path inside him. He asks Link to go inside and break the curse, and Link courageously accepts. And so starts Link's quest to save Hyrule, and even the world, from an evil man named Ganondorf.

The game, as mentioned before, takes place before A Link to the Past, which was the only game in the Zelda series to be released for the SNES. At first, you play as young Link, age 10, but as the game progresses you will have to time travel seven years into the future as adult Link, age 17. You will have the option to freely travel back and forth through time after beating the first temple as an adult, of which there are five. You are free to travel over all of Hyrule, which is huge, and in full 3-D. As you get further into the game, you will obtain new weapons and items that are essential to your progressing, as well as magic spells. You will also get more health as you progress. There are lots of mini-quests and games in Hyrule, such as the archery range, and selling masks, each of which results in some sort of reward. To get by, you will have to use all the smarts and items that you have, because this game is full of puzzles. I can guarantee for first time gamers, that without the use of a magazine, or walkthrough, this game will take you at least 70 hours to complete (and even if you do get help, it will take at least two days). Being the best game ever made for N64, I strongly urge all gamers to at least give this game a try, and then decide for yourselves whether this game is worth all the hype.