This page explains how to start a game of Ocarina of Time.
Create a Save File
Press Start from the title screen to go to the game select screen. Select an empty save file from the menu, or if no empty slots are available, choose an existing game, then choose Erase to delete it.
You will be prompted to enter your character's name. The official name is Link. In the 3DS version, Link is entered by default, but you can delete it and change the name to something else.
After creating a save file, choose it from the menu, then choose Start to begin the game.