After you get the third triforce piece at the third dungeon, you should go to dungeon 4.
Get some Money
You are going to need at least 50 rupees before you go into the fourth dungeon. This is because there is an old man there who will say "LEAVE YOUR LIFE OR MONEY." You can either choose to permanently lose a heart container (unless you only have three, in which case he will just empty your hearts, so you will die the next time anything hits you), or you can pay 50 rupees to get the guy to leave you alone. You should really just pay the guy so you don't permanently lose a heart container, so be sure to have 50 rupees.
You should also try to have have an additional 100 rupees so you can upgrade your bomb carrying capacity, so if possible, bring a total of 150 rupees with you to this dungeon.
Go to the Dungeon
Warp to dungeon 3 (if you aren't there already), then go south, east, north twice, northwest, and west twice. Push the easternmost rock to reveal the stairs to dungeon 4.
Get a Key
Go west from the entrance and light up the room with the blue candle. Then kill all the zols and keese to make a key appear. Take it.
Get the Compass
Go east and north. Use the whistle to make Digdogger turn into three small Digdogger Kids, then kill all three to make the door open.
Go west and kill the Pols Voices and Darknuts to get the compass. Then go north and light up the room with the Blue Candle.
Optional: Get the Magic Book
You can get the magic book now if you wish, although you can only use it after you get the Magic Wand, which is in dungeon 8, so you won't be able to use the Magic Book until almost the end of the game. You might want to just wait, then come back to this dungeon when you have more heart containers. It's your choice. If you don't want it, skip to the next section.
In the room north of where you got the compass, unlock the east door and go through. Kill Aquamentus by hitting its horn until it dies. Then go through the door behind it. Kill the Keese, Pols Voices, and Gibdos, then push the block that is in the middle of the far left. Go down the stairs that appear, and get the Magic Book.
After you get it, go back upstairs, then go west until you can't go west anymore, and light up the room with the Blue Candle.
Get a Second Key
You should be in the room that you had to light up with the Blue Candle. If the north door isn't open, kill all the Darknuts to open it. If you get touched by a Red Bubble, you have to touch the Blue Bubble to be able to use your sword again. When the Darknuts are all dead and the north door opens, go north and kill these blue Darknuts to get a key.
Upgrade your Bomb Carrying Capacity
If you have at least 150 rupees, go east through the locked door. Then push the middle of the east wall until you go through. Pay the old man 100 rupees and you will be able to carry 12 bombs instead of 8. Then push the middle of the west wall until you go through, then go west until you can't go west anymore.
Get a Third Key
From the room with the two statues in the bottom corners, go north and be careful of the spike traps by the door. Go east and kill the Gibdos, Keese, and Pols Voices to get a key.
Get Ten Rupees
If you want ten rupees, bomb the east wall and go through the hole to get ten rupees. Then go west through the hole to return to the previous room.
Optional: Get the Map
If you want the map, go north, push the middle block up, then bomb the middle of the east wall and go through the hole. Feed bombs to the Dodongo until it dies. Get the bombs that appear. The north door will open. Go through. Kill the Darknuts to get the Map.
Then go south, and west. Push the middle block, then go south.
Go west and be careful of the spike traps by the door. Then go north. Use the Blue Candle to light up the room, then kill the Zols to get bombs.
Go to the Dungeon Boss
Go east, and push the middle block. Then go north. Use the Blue Candle to light up the room. If you kill the Keese, a key appears, but you can't reach it right now.
Make sure you have at least 50 rupees. Bomb the north wall and go through the hole.
You need to go through the east door, but the old man won't open it unless he either permanently takes away one of your heart containers, or he takes 50 rupees. Pay the rupees. Then go east through the door that opens.
Push the left-hand middle block to make stairs appear. Go down and follow the passage until you are upstairs again.
If a Red Bubble touches you, you won't be able to use your sword anymore! If this happens, just go down the stairs and follow the passage until you reach the room with Blue Bubbles. Touch one to be able to use your sword again, then go down the stairs and through the passage again.
Go north through the locked door.
Use the whistle to make Digdogger split into three, then attack the Digdogger Kids until they die. Get the heart container and go north, but don't take the Triforce Piece yet.
Get the Raft
You can only get the raft by going through a secret passage in the Triforce room. Push the middle of the north wall to go through.
Kill the Darknuts to open the north door. Go through.
Kill the Dodongos to open the north door. Go through.
Kill the Pols Voices and Darknuts. Note: If one of them drops a clock, you can walk through the frozen enemies without getting hurt. Then push the block that is in the left column of blocks, just above the corner block. Go down the stairs that appear, and get the Raft.
Get the Triforce Piece
Go upstairs from where you got the raft. Then go south until you reach a dead end. Push the middle of the south wall to go through. Take the Triforce Piece.