There are many things to do and items to collect in Kakariko Village before proceeding to the next part of the game.
You can find five golden skulltulas in Kakariko Village at night.
Talk to the girl near the graveyard entrance. The girl there has lost her cuccos and asks you to find them for her.
Be sure not to attack cuccos too much. If you do, a bunch of cuccos will swarm around and attack you until you either die or escape to another area.
Here is how to find the girl's cuccos:
After putting all 7 of the cuccos back into the pen, talk to the cucco girl to receive an empty bottle. If you leave town and go back, you can put the cuccos into the pen to receive 50 rupees from Anju.
Go to the graveyard. It's east of the town well. There is a rock just outside of the wooden fence gate of the graveyard. Pick it up and some bugs will appear. Catch one in your empty bottle. Then go to the left wall of the graveyard and go to the near end of the graves to find a spot of soft soil. Stand on the edge of the spot and drop the bugs into the soil. If you can, try to scoop up one of the bugs that fall out so you can have another in your bottle. The bugs on the ground will crawl into the soft soil, then a moment later a gold skulltula will pop out. Kill it and get the token.
In the graveyard, look for a grave with flowers in front of it near the front of the graveyard. If it's night time and nobody is around, get behind the grave and pull it backward to reveal a hole. Jump in. Open the chest at the end of the room to receive a Hylian Shield. Equip it.
Go all the way to the grave at the far end of the graveyard. Stand on the Triforce symbol and play Zelda's Lullaby to make lightning shatter the grave. Drop in.
Inside the grave, there are keese on the walls. There is one near the door, another on the right wall, and two more on the statue on the far wall. You can use your slingshot to hit them from a distance or just run up and hit them with your sword. Once you kill them all, the door will open. Climb the stairs and go through.
Stay along the left wall. The ReDeads in this room can freeze you by looking at you, then they can grab onto you and drain your life. If you stay near the far left wall, you should be far enough away to run away even if you get frozen.
Go to the passage in the far wall and follow the path. Read the wall to learn Sun's Song.
Go back the way you came. Play Sun's Song in the room with the ReDeads to freeze them all, then exit the grave.
In the row of graves close to the grave where you learned Sun's Song, pull the grave that is the second from the right. Inside, play Sun's Song to freeze the ReDead and kill it, then stand on the platform and play Sun's Song again to reveal a chest that contains a piece of heart.
Pay Dampé 10 rupees to dig in soft spots around the graveyard. At a random spot he will pull up a piece of heart.
If you have 10 gold skulltula tokens, go into the house of skulltula and talk to the one human inside to receive the Adult Wallet, which lets you carry up to 200 rupees.
Read the previous section about how to get a free Hylian Shield from the graveyard. Equip it. Then talk to the soldier guarding the Death Mountain Trail entrance. Show him Zelda's Letter and he will open the way. Go through.