There are twelve songs you will learn in this game, and one secret song you will create on your own. Below, are listed each song you will learn in good order. It's a good idea to memorize these songs, you will use them freqently in the game.
Zelda's Lullaby - Zelda's Nanny, Impa, teaches you this song. You will need this song to open certain places, and to make things happen.
Saria's Song - If you go to the Sacred forest meadow, Saria will teach you this song. Play it to talk to Saria from wherever you are.
Epona's Song - Malon will teach you this song when you are a child. If you play this song, Epona, the horse, will race towards you.
Song of Sun - Learn this song from the gravestone in the Graveyard in Kakariko. Play Zelda's Lullaby in front of the grave right at the other end of the graveyard, and jump inside the hole. Read the message on the wall to learn the song. Use this song to change day to night, and night to day.
Song of Storms - Learn this song from the windmill man as an adult. Go into the windmill and talk to the man. He will talk about some kid from seven ago. Pull out your ocarina and he will teach you the song. Use this song to make it rain!
Song of Time - Learn this song from Zelda as a child. You will need it to become an adult. The song of time will move any blue blocks with a certain image on it.
Minuet of Forest - This is a song you will learn from Sheik. Use it to warp to the Sacred meadow which is where the entrance of the Forest Temple is.
Bolero of Fire - Leart this song from Sheik. Use it to warp to Death Mountain Crater, where the entrance to the Fire Temple is at.
Serenade of Water - Learn this song from Sheik. Use it to warp to the tiny island in the middle of Lake Hylia.
Nocturne of Shadow - Learn this song from Sheik as well. Use it to warp to the graveyard, to the unreachable ledge. The entrance to the Shadow Temple is right behind you.
Requiem of Spirit - Learn this melody from (you guessed it) Sheik. The song will warp you to the entrance of the Spirit Temple. This song ain't good for much else.
Prelude of Light - Learn this song from Sheik when you re-enter the Temple of Time. Use it to warp to the Temple of Time quickly. You can use it when you want to get to Hyrule Market in a hurry.
Scarecrow's Song - If you talk to the scarecrow by Lake Hylia, he will ask you to compose a song that he will never forget. Use this song to make Pierre the scarecrow appear. Use Pierre to get to places you cannot easily reach. Unlike the other songs, this song is one you will make up on your own.