The Goron Lullaby is learned at the Goron Shrine in the Goron Village from the Goron Elder. After talking to him, he will offer to teach you the first six notes but can't remember the ending of the song. This will teach you the first part of the song called the Lullaby Intro. If you then take the song the Goron baby and play it for him, he will teach you the last two notes which will complete the song.
The song is used primarily to put people and Gorons in particular to sleep. The most important use of the song is the open the path to Snowhead Temple. Playing this for the Goron in front of the path will put him to sleep and allow you to pass.
