Outset Island
The game will start with Aryll waking you up and telling you to go to Grandma's House. Before you do, I recommend that you look around the island- it can teach you lots of things about controls, and there are several rupees for you to get. I particularly recommend the pigs minigame, which you can start by talking to the woman by the house on the hill, and which can earn you 60 rupees altogether.
When you go to Grandma's House (the furthest one away from you), you will be given your Hero Clothes, and she'll tell you to fetch Aryll. Head back to where you started, and Aryll will give you your birthday present, her Telescope. She'll tell you how to use it, and first to look at the red postbox. Do as she asks, then look up into the sky, and you'll see a giant bird, the Helmaroc King, kidnapping a young girl. The bird will be hit by a cannonball and drop the girl into the forest.
Aryll will say you need something to defend yourself with, so head to Orca's House. It is the bottom floor of the two- storey house near the middle of the island. Speak to Orca, and he'll give you a short swordplay tutorial- just do everything he asks. Once you've completed it, Orca will give you the Hero Sword. If you L-Target and 'Check' the crest on a shelf above the shark, he'll tell you about the Knights Crest, and ask you to collect 10 of them. You shouldn't worry about this too much, though, since you can't complete it until much later in the game.