After you complete the Triforce, you should fill your hearts and bombs, get medicine, and go to the final dungeon and save Zelda!
Complete the Triforce
You won't be able to enter the final dungeon if you don't have all eight pieces of the Triforce. If you don't see a completed Triforce when you press START to go to the item screen, you need to complete whichever dungeon or dungeons you might have missed, until you have all the Triforce Pieces.
Get all Heart Containers
Be sure to get all the Heart Containers in the game before you go to the final dungeon. See Heart Containers to learn their locations.
Get Arrows
You won't be able to win the game without arrows, so if you don't have any, be sure to look for shops around Hyrule that sell them. (And if you don't have the bow, you need to go back to Dungeon 1 and get it!)
Upgrade Your Sword
If you don't have the Magical Sword, read Get the Magical Sword for instructions on how to get it. (And if you don't have a sword at all, you will need to at least get the Wooden Sword if you want to defeat the final boss.)
Upgrade Bomb Capacity
Bomb upgrades are available in Dungeon 5 and Dungeon 7, for 100 rupees each. After you get both upgrades, you can carry up to 16 bombs.
Get Medicine
If you don't yet have the letter to the old woman, get it from the northeast part of Hyrule. If you don't have it, you can warp to Dungeon 2, go south, then east, then north, north, and northeast, then go east, then go up the stairs and go into the cave to get the letter. Then you can go south, west, north, and bomb the north wall to find a cave where there is an old woman selling medicine.
You can also warp to dungeon 3, then go west, north, and east, and go into the cave to get medicine.
The red medicine is better because after you refill your hearts with it, it turns into blue medicine, so you can refill your hearts with it a second time. The blue medicine turns back into the letter after you use it.
Get Rupees
You should have some rupees with you before you go, because you need to have them in order to shoot your bow and arrow.
Go to Death Mountain
Warp to Dungeon 1, then go east. From there, go north, west, and north. Walk across the river (the stepladder lets you do this), then go up the stairs. Go west twice. These two big rocks are Spectacle Rock, where Dungeon 9 is hidden.
If you need medicine, go west from Spectacle Rock and go into the cave to buy medicine. Then go east to Spectacle Rock.
Bomb the south wall of the left rock to open the dungeon entrance, and go inside.
Get the Compass
Go north from the entrance. If you have gotten the Triforce Pieces from all eight dungeons, the doors will open for you. (If not, the old man will tell you that you need all the Triforce Pieces, and you will have to go back and complete whichever dungeons you missed.) Go north, then bomb the middle of the west wall and go through. Kill the two Lanmolas, then push the leftmost block up or down, and go down the stairs. Follow the passage until you are upstairs again.
Go around the spiral and go through the east locked door. Use the Candle or Wand to light up the room. If you want the Compass, bomb the south wall and go through (kill the monsters here to get more bombs if needed), then bomb the south wall and go through. Kill the Wizzrobes to get the Compass, then go north twice.
Get the Map
Use the Candle or Wand to light up the room, then go east. You can kill the Patra (start by killing all the small ones) to get more bombs.
Go south, then bomb the middle of the east wall and go through. You can kill this second Patra to get the Map.
Get the Red Ring
Bomb the middle of the north wall and go through. Then in the next room, also bomb the middle of the north wall and go through. Kill all the Wizzrobes and push the leftmost block up or down, then go down the stairs. You will get the Red Ring, which increases your defense even more than the Blue Ring.
Get the Silver Arrows
Go upstairs, then go south twice, then go west, then north. Unlock the north door and go through. After the old man finishes talking, bomb the middle of the west wall and go through. Kill the Wizzrobes and push the leftmost block to make stairs appear. Go down. Follow the passage until you are upstairs again.
Go west through the locked door, then go west again. Kill the Patra, then push the leftmost block up or down, and go down the stairs. Follow the passage until you are upstairs again.
Bomb the middle of the north wall and go through. Kill the Wizzrobes, then push the middle block on the right side to make stairs appear. Go down the stairs to get the Silver Arrows. Then go back upstairs.
Go to the Dungeon Boss
Go south, then kill all the Wizzrobes, then push the leftmost block up or down and go down the stairs. Follow the passage until you are upstairs again.
Go north, then kill all the Like-Likes to open the west door. Go through.
Use the Candle or Wand to light up the room. In the room with the Zols, go north through the locked door. Then in the room with the Wizzrobes, go north through the locked door.
Avoid the spike traps at the door, then kill all the Wizzrobes, then push the leftmost block to make stairs appear. Go down the stairs. Follow the passage until you are upstairs again.
Bomb the middle of the west wall and go through the hole. Kill the Zols and Like-Likes, then push the leftmost block up or down and go down the stairs. Follow the passage until you are upstairs again.
Kill the Patra to open the north door, then go through.
Ganon
You will show your Triforce of Courage, and Ganon will appear. Then he will become invisible. There appear to be holes in the floor, but you can walk over them. You can only tell where Ganon is by looking for the fireballs that he shoots at you. Swing your sword where the fireballs are coming from. After you hit Ganon enough times with your sword, he will turn red and be stunned. While he is stunned, hit him with a Silver Arrow to kill him.
Rescue Zelda
Then take the Triforce of Power that he left behind, and go north, kill the fire with your sword, and go to Zelda! Congratulations! You're the hero of Hyrule! Wait until after the credits roll, and press START. Your saved game will have a sword next to it, and if you play it, you will start the Second Quest.