At the main menu you’ll need to start a New Game. The default name for the hero is Link.
As you progress through the game you may save, the main menu will adjust accordingly and you may now load one of three files available. At this point you may choose Options and adjust the game settings as you need.
To save your game you’ll need to find a stone statue shaped like an owl, commonly called an Owl Statue, or one of the newly-added Quill Statues (an Owl Statue with the owl replaced by a quill).
In the original game returning to the Dawn of the First Day would automatically save your game, in this edition that doesn’t hold true.
You can delete files from the main menu one at a time, while holding A + B + X + Y at the same before the title screen appears will clear all data.