Instructions
Enter the Hyrule Market using the map the owl gives you in Hyrule Field. The drawbridge at the entrance closes at night, so search the nearby area for cash and items while you wait for daybreak if you reach the market during nighttime hours.
Talk to everyone in the market, especially a young girl named Malon looking for her father. Walk to the castle and talk to the guards who tell you nobody is allowed in. Walk back into the market and then return to the area with the guards to make Malon appear there. Talk to her again. Then climb the wall behind her and drop down the ladder to get into the castle.
Keep walking until you come to some water. Swim around the pillar to the end of the water and jump out by the sleeping man, Malon's father Talon.
Push and pull the blocks behind Talon to make a bridge that will let you jump onto the ledge by the water.
Sneak across the courtyard following the path, hiding behind bushes as the guards come near.
Talk to Zelda who is standing at the end of the path to get Zelda's Letter.
Present Zelda's Letter to the guard at the entrance of Death Mountain, and he will open the gate.