The gigantic Goron Vase is found in Goron City on the bottom level, just outside Darunia's room and the Goron Shop. If Link lights all the unlit torches in the city, the vase will start spinning. If Link throws a bomb into the vase, it will spin around rapidly, stop, release some items, and resume spinning. Which items Link receives depends on which face the spinning vase ends up on when it stops spinning, which again depends on the timing of Link's throw. The angry face will yield three Rupees; the smiling face provides 10 bombs times three; and the happiest face will earn Link a Piece of Heart and two Red Rupees.
Five Goron Vases are attached to the chandelier in the Goron Shrine. Inside one is a hidden piece of Rock Sirloin. If Link lights all the torches in the shrine, the chandelier will start spinning, allowing Link to break any of the vases by rolling off of a ramp at full speed while in Goron form. If Link breaks the correct one, the Rock Sirloin will fall out; it can then be brought to the Hungry Goron.
The Goron Vase is obtained after giving the Rock Brisket to the Goron guarding the staircase south of the Goron Dance Hall in the present. It is then given to the Goron in the same location in the past in exchange for Goronade. This vase was claimed to belong to the ancestor of the Goron that Link got it from. This likely means that it is paradoxically the very same vase Link gave to the Goron in the past.
The Goron Vase is given to Link after he feeds Biggoron Lava Soup, clearing the Goron's head cold. The Goron Vase can then be given to Ingo, who is an avid vase collector. In exchange, he trades him his Fish, as part of the trading quest for the Noble Sword.