Instructions
Head to Goron City via Death Mountain. When you enter the city, you can go through the winding paths until you reach the bottom or dump down to tuck and roll. Either way you go, head down to the bottom of the city.
Head to the carpet with the Triforce symbol on it and play Zelda's Lullaby on the Ocarina. Enter the room that this opens and speak with the Goron inside.
Play Saria's Song for the Goron, whose name is Darunia, and he will give you the Goron Bracelet. This allows you to pick up bombs.
Leave Darunia's room and head up the winding paths to the top of Goron City. You will eventually encounter a Goron rolling around in a ball. Go to the bomb flowers nearby and pick one up. Leave the bomb in the Goron's path so that it explodes just as he's passing by.
Speak with the Goron once he stops. Talk to him about the Dragon and the Gorons -- these are options you have during the conversation -- and he will give you the Goron Tunic for free.