With his last breath, Agahnim sends you to the Dark World, on top of the Pyramid. In the Dark World, you must find and rescue Zelda and the other six maidens, being held by an even stronger force.
Go down the first two sets of steps and jump off the ledge to the Pyramid's first level. Walk along the edge to the east until you find the Heart Piece, which should raise your life to ten Hearts. Then head off the Pyramid and go east to the hills.
The monsters in the Dark World are much stronger, so be careful. There aren't many places you can go yet other then The Dark Palace, but you can go north to the shop and transport back to the Light World Potion Shop for more medicine. (There is medicine in the Dark World shop, but it's cheaper in the Potion Shop)
Go south of the hills and follow the trail to the forest maze. In the shrine in the middle you'll meet a talking tree that will tell you a little about the Golden Power. Bomb a hole in the north wall to find some hearts. To the east of the shrine, you'll find arrows in the ground that show you where to go. Once you go around the shrine, don't take the first entrance you see into the trees but take the underpass to the outer path and then the second underpass to the second entrance.
The path through the trees is pretty simple - just follow along the openings in the foliage. When you make it out the other way, you'll meet Kiki the Monkey. Give him the Rupees he wants and he'll follow you. Continue on the path east until you reach the Dark Palace. Only Kiki can open the door, and he'll want 100 Rupees to do it. Give him the money and enter the palace.
The East Palace is far more challenging than the dungeons you've been through so far. First, go through the right door, down the stairs and through the warp. Take the south door and bomb the wall at the end of the path. In the room past the moving floor, the blue Goriyas can be taken out with the sword, but the red one requires arrows and you can't shoot him head on or he'll shoot fire at you. Since he only moves when you do, shoot an arrow and make him walk into it. Once the Goriyas are gone you can get the map in the next room, then bomb the crack in the west wall to get a key.
Return all the way to the entry room and this time take the left door and down those stairs. In the lower room, hit the switch under the skull in the lower corner to get the key. Go back up and open the center door on the first floor. Be careful of the monsters you meet in the next room - the jellyfish shouldn't be hit when they're flashing, and you can't hurt the turtles for now. Take the right door. Get the key from the chest, go back to the previous room and take the left path.
Bomb the cracks in the floor and jump down the hole to the basement. Open the door and go up the stairs to find the Big Key. Go back down the stairs and jump off the ledge, then hit the switch under the skull in the center to get the chest with another key - watch out for the Stalfos whose heads fly off at you. Take the warp in the room and you'll be back in the first warp room you found.
Retrace your steps to the first floor middle room with the two paths and take the right one again. Jump down the ledge past the chest to the next path and open the door in the west corner. In the next room, go across the path before it completely falls off and open the door to your left. Make your way through the dark maze to the lower right corner of the room. Get the key in the chest there, then bomb the crack in the middle of the east wall to get to the Big Chest with the Hammer.
Return to the room with the falling path and take the right door to get the compass, then take either of the stairs to the north. You'll find several Rupees, arrows and another key in the dark room. Go back upstairs, open the south door and go back to the big room with the multi-level floors. Jump down to the middle floor and hit the globe with the boomerang, and you can reach the east door.
Clear the skulls in the to right corner of the room to find the switch, then push the top right statue all the way on top of the switch to open the door and keep it open. Defeat the Goriyas the same way you did the others to open the door. In the next room, hit the globe if you can't get past the posts. Shoot the Goriya statue in the eye and the east wall will move away to reveal the stairway.
Use the hammer to get past the bobbing pegs. You can also use it to knock the turtles upside down, leaving them vulnerable. Use the boomerang on the globe to make your way to the door. Follow the path to the room with the many turtles and take them out with the hammer - it will be easier if you light the torches first. In the next room push the upper right corner block to get to the warp that will take you to the big door.
Helmetsaur is one of the toughest boss monsters you'll face. Run to a corner to avoid his swinging tail. His fireballs are pretty easy to avoid, even as they split apart. You have to throw bombs at his mask to blow it off. It's near impossible to time your throw so it blows up at the right time and not get hurt yourself. Once the mask is gone, hit the emerald on his head, using the spin attack when you can.
When Helmetsaur is defeated, he will leave a Heart Container and the first crystal. The maiden inside will tell you more about the Golden Power, where the other maidens are, and who is truly behind this evil plot.