Instructions
 
Play through "Ocarina of Time" as normal until Link pulls out his second sword. This is part of a cutscene during the story and cannot be missed. 
Head to Goron City, located on your in-game map. 
Walk to the third floor to find a small Goron running around with a bomb. Walk up to him and press "A" to initiate conversation. He and Link discuss dragons and Gorons, and he gives you the Goron Tunic upon completing the conversation.