Visit the village, then head for the Kakariko Graveyard south-east on the map. During daytime, talk to the kid, then, at night, pull the second grave in the first row (there are yellow flowers in front of it) and jump into the hole to get a free Hylian Shield! Then go to the back of the graveyard, read the steles surrounding the main tombstone, then play Zelda's Lullaby in front of it. The tombstone will open, go down, get rid of all the bats, open the door and go through the room while avoiding the ReDeads. Look at the stele to learn the Sun's Song. Leave the graveyard and go to the gate north on the map. Hand over Zelda's Letter to the guard who will give you a discount on the Hylian Shield (not so useful anymore) and will ask you to find a mask for him. Before going on, you can find two Pieces of Heart in the graveyard. You can also get another Bottle by bringing all seven chickens to their pen.
Death Mountain Trail
Go through the gate, speak with the Gorons (the friendly-looking rocks) on your way and go ahead until you reach the red flag. Then follow the path on the right to their village.
Take the different passages to reach the lowest floor. You can also walk on the rope and let yourself fall (ouch!). Stand in front of the ornamented door, play Zelda's Lullaby and get in. Speak with the Chief Darunia and play Saria's Song for him. He will reward you with the Goron's Bracelet which allows you to carry and toss Bomb Flowers (green plants withholding bombs). Light a Deku Stick, get out and light the four torches in each corner of the courtyard to activate the giant statue. In order to reach the shop, light another Deku Stick and set the two Bomb Flowers on the wall on fire. Take note of a path blocked with rocks (two floors under the entrance, the level with the red-lined poles), if you clear this passage, you will get a shortcut towards the Lost Woods. Go back to the Death Mountain Trail.
Death Mountain Trail
Before walking down the path, go right, there is a Bomb Flower near a fence. Take it and throw it so it blows up the cave's entrance below. Then go down to the cave and get in.