Zora's River
From Kakariko Village - head south and following the small river. Stay by the wall and head left at the fork to reach Zora's River. Continue up the path to find Kaepora Gaebora. After speaking with him - bomb the boulders. Go down the path and grab the Cucco. Fly across to the other ledge and continue down the path.
Head left and jump onto the ledge that is higher up. Continue going down the path to the right. Drop the cucco if you have not already and climb up the small ledge on the east of the map. Travel through the small flow of water and climb up another ledge. Continue east across some more water. Head up the hill and across the small bridge.
At the end of the path will be several rows of land. Climb up to the center of the first one and jump down to the next. Continue until you come to the Triforce symbol. Play Zelda's Lullaby and the waterfall will separate - unlocking the entrance to Zora's Domain. Jump across to the door to enter it.
Zora's Domain
Travel down the path and to the top of Zora's Domain, where King Zora will be located. Head down the path to the left of him to find a lone Zora. Talk to him and agree to play the mini-game. Jump from the waterfall and start collecting the rupees. You must dive down to each of them. After doing so - go talk with the Zora again to get the Silver Scale.
Jump back down from the waterfall and dive into the small exit in the bottom of the water. You will come out in Lake Hylia. Swim forward some to find an Empty Bottle on the bottom of the lake. Dive down and collect it. Now head back to Zora's Domain and up to King Zora. Target King Zora and show him the bottle, which actually contains a letter from Princess Ruto.
Now travel back down to the middle level of Zora's Domain. Travel around to find a small amount of water with fish swimming in it. Use the newly acquired Empty Bottle to catch a Fish. Travel back to the top of Zora's Domain and head pass King Zora to find Zora's Fountain.
Zora's Fountain
There is not much to do right now in Zora's Fountain. You will find a giant fish - Lord Jabu-Jabu. This is the location of the next dungeon of the game. Simply release the Fish from the bottle in front of Lord Jabu-Jabu to be sucked inside Jabu-Jabu's Belly.
Part 4: Dodongo's Cavern | Part 6: Inside Jabu-Jabu's Belly
