Death Mountain Trail
Go back near the red flag, climb the hill, then blow up the rocks to go right. When rocks start to fall from the sky, use your Hylian Shield to protect yourself. Go ahead, climb to the top of the wall and you will meet the owl again. First of all, blow up the wall to the left of the owl and get into the Great Fairy's Fountain. Play Zelda's Lullaby on the Triforce symbol and the divine Fairy of Power will appear. She teaches you the Spin Attack and you will also get a magic meter. Get out and talk to the owl so he brings you back to Kakariko Village.
On the roof, walk slowly to the right and jump on the roof of the chicken house. Enter the hole in the wall to find a Piece of Heart. Then leave Kakariko Village and go back to Hyrule Castle through the Market.
Hyrule Castle
Go near the huge rock in a dead-end east on the map and blow it up using a Bomb. On the other side of the path you will discover another Great Fairy's Fountain and you will get Din's Fire.
Go back to the Hyrule Field, walk past Kakariko Village, cross the river and you will see a sign indicating Zora's River.