As you continue up the trail, you will come to a place where the path opens up. A wide, steep path leads to the left, and a small path leads to the right. The left path, which leads to Death Mountain summit, is blocked by boulders. It is impassable to you at the moment, so head to the right. The path begins to descend, and you'll pass a circular group of stones. Beyond them is the entrance to Goron City.
As you travel up the mountain, speak to the various Gorons found around the city. They'll tell you that Ganondorf has sealed up the entrance to Dodongo's Cavern. That's where the Gorons get their food. Ganondorf has said that he won't remove the boulder until the Gorons give him the Goron's Ruby.
Getting to Goron City
Work your way up the trail to reach Goron City. You can talk to the various Gorons you meet here to hear of their plight. On the way up, watch out for a rather wild Goron rolling down the hill. Most of this area is impossible to reach without bombs, so it's a straightforward path to Goron City, but you can get one Heart Piece if you're crafty (you can get it later another way if you're not willing to bother now). After having a chat with the Gorons, head inside Goron City to meet Darunia.
Goron City
Once inside Goron City, you can talk to many Gorons who are scattered throughout. Most of them will tell you about how hungry they are and go back to sleeping. Head to the bottom floor of this cavern by finding the steps on each floor, or by just jumping down from the top. Once there, head for the locked door with a rug in front of it.
Darunia's Anger
Darunia, the head Goron, has locked himself in his room at the lowest level of Goron City.
After arriving at the door, Link notices a mat with the symbol of the Hylian Royal Family in front of it. Link figures out that, like every encounter with this symbol, as a royal emissary, he should play Zelda's Lullaby to proceed. After the music is played, the door will open on its own. However, when you speak to Darunia inside, you find that he is in an awful mood. He refuses to explain the problem. He claims that it is a "Goron problem" and should not be discussed with Hylians.
Note: If Link has already been through Lost Woods to get Saria's Song, Link should play that song to Darunia to sooth his anger. He will then give Link the Goron's Bracelet which allows Link to carry heavy objects such as the Bomb Flower. This is important because a Bomb Flower is required to blow up the large boulder blocking Dodongo's Cavern.
Livening Up Goron City
| Goron Shop Items | ||
|---|---|---|
| Item | Quantity | Price (rupees) |
Bombs 
|
5 | 25 |
| Bombs | 10 | 50 |
| Bombs | 20 | 80 |
| Bombs | 30 | 120 |
Goron Tunic 
|
1 | 200 |
| Red Potion | 1 | 40 |
| Recovery Heart | 1 | 10 |
| Recovery Heart | 1 | 10 |
After speaking with Darunia, go outside. The Goron outside says that Goron City is exciting when the fires are lit. You use a Deku Stick with the fires in Darunia's room to light the other torches. This causes the central jar to rotate and music to play. It also provides you with sources of fire, which you can use to light Bomb Flowers. Light the bomb flowers on the lowest level and a doorway opens up. Inside is a Goron Shop, although there isn't much you're interested in right now.
To the Lost Woods
A Goron on the second level says that all Gorons enjoy the music he hears coming from the passage near him. You notice boulders blocking the passage, but also Bomb Flowers growing around the boulders. Using a Deku Stick, take fire to one of the flowers. The passage is now clear. Upon entering, you find yourself in the Lost Woods.