Head to Goron City by walking along the outer edge. Jump over the ledge until you're at the bottom. Navi will turn green and point out a mat on the floor. Stand on it and play Zelda's Lullaby to open the door to King Darunia's Chamber. Speak with Darunia and then play Saria's Song. He will give you the Goron's Bracelet. This bracelet gives Link the ability to pick up bomb flowers.

Guide to Goron City
You can do a little more now that you have the Goron's Bracelet. Once you find the Bomb Bag in Dodongo's Cavern, you'll have total freedom.

Boulder Room
On the top floor of the city, you'll find a room that is blocked up by boulders. Bomb them to find more boulders. You can only bomb the light brown boulders, the dark-brown boulders can only be broken with the Megaton Hammer.

MediGoron's Shop
On the next floor down, another room has bee walled off. Use a bomb flower to blow it up. The Goron here says he's working on "something special" and to come back in 7 years. The item he is talking about the Giant's Knife which you can buy from him for 200 Rupees as an adult.

Goron Shop and Revolving Vase
On the bottom floor of Goron City, you'll find a bombable wall which leads to the Goron Shop. You can't enter the shop unless you have the Bomb Bag or a bomb flower. Use Deku Stick to light all the torches around the vase there, it will begin to spin. Throw a bomb into the vase and a Piece of Heart may pop out. Come back with the bomb bag to do all this.

Goron Shop
Item-Cost
Bombs-5 for 25 Rupees
Bombs-10 for 50 Rupees
Bombs-20 for 80 Rupees
Bombs-30 for 120 Rupees
Goron Tunic-200 Rupees
Recovery Heart-10 Rupees
Red Potion-40 Rupees

Lost Woods Warp Point
Bomb the boulders blocking the entrance to the Lost Woods Warp Point.

Now that you have the ability to pick up the bomb flowers, leave Goron City and go you're your right, to the edge of the cliff. Pick up the bomb flower and throw it over the edge. This should blow the boulders blocking the entrance to Dodongo's Cavern. It may take a few tries. The bomb flower regenerates after a few seconds. Position yourself at the proper angle and do a backflip over the fence and onto the ledge above the cavern. Pick up another Piece of Heart there! Normally you must be anadult to get that Piece of Heart but why wait? Jump down and enter Dodongo's Cavern.