Dragon Roost Cavern
Before you enter the dungeon proper, you'll need to cross the small lava river blocking the way. Note the two statues holding vases on either side of the river. Pick up a bomb flower and throw it into the vase on the right. Now pick up a second bomb flower and jump onto the newly created platform. Throw the second bomb into the vase on the left, then jump across. Enter the cavern.
Dragon Roost Cavern: 1F
In the first room, you'll see three statues on large blocks in front of a symbol on the far wall. Pull the first block out, then the second behind the first, revealing a doorway. In the next room, you'll fight two bokoblins. After you've defeated them, grab a stick and set it alight with one of the torches. Use the flaming stick to light the two unlit torches, which will make a chest appear. Get the key from the chest and open the locked door. Before leaving, note the warp pot in the room. These serve as waypoints in the dungeons and will let you teleport forward if needed.
Slash through the boards blocking the next passageway. Make your way to the large cavern and go west along its border until you come to a block. Pull the block and climb up, then continue. Cross the long bridge until you reach the boulder. Pick up a bomb flower and throw it at the boulder, then proceed through the doorway.
If you break the jars in the next room, you'll notice they are full of water. Pick one up and throw it on the lava to create a platform. Jump over to the chest to get the dungeon map, then pick up another pot, throw it on the lava, and jump to the other side. In the next room, you'll come across another boarded door. After you kill the bokoblin here, you can use his sword to break the boards. Take the sword into the next room, where you will fight two red chuchus. Throw the sword up to the ledge, and then climb up and break the boards to access the chest, which contains a key.
Return to the room where you got the bokoblin's sword, and go through the door to the north. You'll be back in the large cavern. Throw a rock at the bomb flowers on the wall, which will explode and destroy the nearby boulder. You'll be back near the door through which you first entered the cavern, but this time you have a key. Unlock the door. Beyond it, you'll fight another bokoblin. Take his stick and light it with the torch, then burn the boards blocking the door. Step on the switch, and head outside through the door to the west.
Cross the bridge, but don't fight the bokoblin on the bridge if you can help it. Try to get past him before engaging him too seriously--fighting on bridges is dangerous, as you can fall off or cut the ropes. Climb the ladder, and avoid the fire stream that occasionally blocks your passage. When you reach the top, you'll fight a kargaroc, which will drop a golden feather. Sidle across the nearby ledge, again avoiding the fire emitting from the hole in the wall. You'll come to a ledge above you. Jump up and shimmy along, and then continue up. Grab a bomb flower and toss it at the rock below. This will reveal a door. Go through it and back into the cavern.
You'll see a huge stack of blocks in the next room. Pull on the blocks to create a makeshift stairway, and climb up.