Exit Goron City and hang a right to see a Goron and a bomb flower. Pick up this bomb flower and throw it over the edge, where it will land outside the entrance to Dodongo's Cavern, blowing up the giant boulder. There is a Piece of Heart you can get now, which usually requires an item later. Get rid of the bomb flower, then stand where it was and look towards the wall at angle; turn around and do a backflip towards the cave entrance to hopefully land on top where the Piece of Heart is.
Drop down and head inside the dungeon. The first thing to do is pick up a bomb flower on either side and blow up the discolored wall. Head inside the actual dungeon, taking note of the bunch of lava, which will burn your Deku Shield if it's still equipped. For now, head to the left side of the big open room and use a bomb flower to blow up the wall in the middle, which reveals a chest with the Dungeon Map inside.
There's a new enemy here, which are the Beamos. They slowly turn their eye around and if they see you, then they will fire a laser that will follow your movements until you get out of range or kill them. After getting the map, head across the platforms, to the other side of the room. Kill the Beamos with the bomb flower, then use another to blow up the wall ahead of where the Beamos was.
In this next room, go all the way to the end, either ignoring the Baby Dodongos or killing them, noting that they explode when killed. You'll find a switch that opens the door, but it resets as soon as you step off it. Grab one of the statues and drag it onto the switch, which should keep the door open. Go through the door, killing the Keese, then through the next door.
You'll now be in a big room with a bunch of platforms, and you'll have to fight a new enemy here (well, actually two of them). They're called Lizalfos and are not easy one-hit kills like the other enemies have been so far. They will continually jump over you and attack from behind, but as long as you're guarding with the Hylian Shield, they can't hurt you. Every three hits you do against one, it will jump away and the other will come after you.
Once they're dead, head through the next door that opens, ignoring the bombable wall at the beginning (only Business Scrubs inside). There's another new enemy here, which are called Dodongos. Their tail is the only spot where you can damage them, and they breathe fire. When you hit their tail, they'll whip around and try to breathe fire on you. When they die, they explode just like the Baby Dodongos.
Your goal in the room with the Dodongos is to light the three unlit torches, which will open the door. Step on the switch in the hallway, which will open a door on the other side of the room. Head over there and go through the door, where you'll see a large structure and A LOT of bomb flowers surrounding it. Ignore it for now and bomb the wall on the southern end of the room, revealing a door.
When you step into this room, the door will close behind you. There's another new enemy here, called the Armos. It's posing as a statue and when you get close, it will come to life. You can either use a bomb flower to destroy it, or use a combination of a Deku Nut and Deku Stick to kill it. Note it explodes when killed. Open the chest that appears to get the Compass.
THE BOMB BAG
Go back to the previous room and notice that there's a slight gap in between the bomb flowers at the base. Pick up one of the spare bombs and place it in between the two rows. When the explosions are all over, a set of stairs is revealed. Climb the stairs and kill the Skullwalltula, then grab the Gold Skulltula above it. Go into the door behind you.
In this room are Fire Keese flying around, so either shoot them with the Slingshot, or block them with the Hylian Shield, which douses the flames, leaving them vulnerable. There are four Armos statues around the land in the middle, but the one guarding the ladder is the only one that isn't real. Pull it away, climb the ladder and step on the switch, going through the now opened door.
You're now on the second floor of the main room of the dungeon. Ignoring the Fire Keese, run across the wooden bridge, jumping over the gap, and head into the next room. There's yet another new enemy here, the Bladetrap, which cannot be destroyed, so just avoid them. You'll find a pushable block on the one side of the room, which you can use to climb the ladder and get to the ledge with the bomb flower. You need to time the bomb flower, so it blows up in mid-air, destroying the wall where you climbed the ladder.
Head through the newly opened path, where you'll see a pillar of flame in the middle of the room. Equip your Slingshot and use it to hit the eye switch above the doorway at the opposite end, which will temporarily put out the flames. Go through, avoiding the Baby Dodongos, and into the next room. This room has another two Lizalfos, so do what you did earlier to defeat them.
With the next door open, go through it and you'll see some more pillars of flame. Shoot the eye switch straight across to disable the first pillar, then hop on that platform and shoot the next eye switch to your left. Go straight ahead, jumping over the gap and climb onto the ledge to grab the Bomb Bag from the chest.
Step on the switch to make an elevator go from the ground floor to where you are, which helps in case you fall. For now, though, go to the right and go onto the wooden bridge. You need to drop bombs into the gaps in the bridge, which will fall into the eyes below, making them turn red. When both are red, the jaw will open and you can go inside.
Before you head into the skull, head to the room where you first encountered the Baby Dodongos and use a bomb to blow up the wall on the right side. Go into this room and kill the three Keese and Gold Skulltula, then use a jumping attack or backflip to collect the token.
Head into the skull, and go to the right, which is the only path you can go right now. Keeping an eye on the Fire Keese, jump down and climb onto the pullable blocks. Throw a bomb to blow up the wall, then go into this room to grab the Gold Skulltula, which is guarded by an Armos. Go back to the previous room, climb the blocks and run along the ledge to the next opening.
Follow this passageway, and push the block into the room below you. Kill the Fire Keese, then pull and push the block into the hole in the center of the room. This will keep the switch pressed so the room going to the boss will remain open. Go through the door, placing a bomb on the discolored section of the floor, revealing the way to the boss.