After going through Zora's River and opening the waterfall with Zelda's Lullaby, you reach Zora's Domain.
Walk along the ledge inside of Zora's Domain, then take a left when the path splits. You will reach a big guy in a red cape. This is King Zora. You can ignore him for now. Go left into the cave and talk to the Zora here. Pay to play the diving game.
When the countdown begins, jump straight off of the edge to dive down below. Swim around so that your shadow is directly over a rupee and press A to dive down and get it. Get all five rupees this way. When you have found them all, the Zora above will call to you. Go back up and talk to him to receive the Silver Scale, which lets you dive deeper than before.
Go to King Zora's chamber and light a deku stick on a lit torch. Run down the stairs and light the unlit torch there. Continue down the path and take a left. Light the torch in front of the Zora shop, then follow the path into the shallow water. Light the unlit torch in the water, then stay close to the far wall and run behind the waterfall. Light the unlit torches here to reveal a chest that contains a piece of heart.
Across from the waterfall, there is an underwater cave opening. Swim to it and dive to go inside. You will emerge in Lake Hylia.
You will see something in the water ahead. Dive to it to retrieve it. The bottle contains a letter from Princess Ruto.
Go to the house on the hill and find the soft soil in front. Drop a bug into it to get a gold skulltula. Plant a Magic Bean here if you have one.
Go to the eastern part of the shore. There are a couple of scarecrows there. If you use the Ocarina near them, they will remember the song that you play. This will help you later in the game.
The song must be eight notes long. You can make it something easy to remember, like C-up C-left over and over. For something more fun, here is the beginning of the Kakariko Village song. Note: you have to press up on the control stick when you play C-down (or R on 3DS) in order to turn it into the correct note.
Scarecrow's Song is recorded in real time, so any pauses that you make between the notes will be recorded, and the notes will be played for as long as you press the button.
Go to the door in the wall east of the scarecrows. Go inside and pay to go fishing. If you catch a big enough fish, you will get a piece of heart. The biggest fish usually stays near the logs underwater near the center of the pond. Cast a line and reel it in until you get that fish to follow. Reel slowly when it is following, then tap A to try to get it to bite. Once it does, hold R and B to reel as quickly as you can. Press left and right on the control stick to try to pull the fish toward you. Watch the fish closely so that you pull left when the fish is facing left and pull right when the fish is facing right. If the big fish gets away, it will swim around in deep water for a while before returning to the logs in the middle.
If the game says that you caught "a real lunker," that means that you caught a big enough fish to get a piece of heart. Talk to the guy to get the fish weighed and you will get the piece of heart.
Swim to the small square island near the middle of the lake. Turn it to night and kill the gold skulltula that appears.
Go back to Zora's Domain. Go to the shallow water near the Zora shop on the lower level and use an empty bottle to catch a fish. You will need it soon.
Show Princess Ruto's letter to King Zora. He will slowly scoot over, giving you access to the passageway behind him. Go through to reach Zora's Fountain.
Near the southeast wall of Zora's Fountain, there is a tree that you can roll attack to find a gold skulltula.
Bomb the boulder near the tree in the southeast part of Zora's Fountain to open a great fairy fountain. Play Zelda's Lullaby on the Triforce Symbol inside to receive Farore's Wind. It lets you create a warp point in a dungeon, allowing you to return to that spot later.
If you didn't catch a fish in a bottle earlier, do that now. Then go up to Lord Jabu-Jabu and drop your fish in front of his mouth. Jabu-Jabu will inhale the fish, and you.