Before you do anything, make sure you have a potion on hand. You'll need this in Zora Village. You can purchase one from Syrup's Shop in Yoll Graveyard.
Alright. First, you have to go to Lynna City (present). Go south from the mermaid statue, and then move left a screen. You'll see some steps going into the water. You need to swim down three screens, then left a screen. Here, you'll see a house on an island-like thing. As soon as you walk up the steps, play the Tune of Time and go to the past. When you get there, you'll realize that in the past, the island was more to the right. Walk out of the water, down the steps, and get back into the sea water. Go left two screens and you'll notice some stairs at the top of the screen. Walk up them, going up one screen, and walk all the way to the top-right corner of this island. Play the Tune of Time again to go back to the present.
You'll reappear in the present in the sea water, where you then have to press B and go underwater. There's a path to the right that you have to follow. So, go right one screen once underwater, and swim down. There's a block that you have to use the Switch Hook on. Once you get across, press B again to resurface, and walk up the steps and onto the island. Play the Tune of Time again to go back to the past.
When you reappear in the past, go left one screen and go underwater. Continue left one more screen while underwater, and go down one screen from there. Resurface here and walk up the steps onto the isle. You can go ahead and play the Tune of Time on the steps, sending you back to the present, where you'll reappear in some water there. Go underwater here, swim down one screen, and use the Switch Hook on the block to cross. Move left one screen and you'll be in Zora Village.
Now in order to get to the next dungeon, which is in side Lord Jabu Jabu's Belly, you have to do a few things, but I'll make it pretty short. You have to go to the past in Zora Village (resurface and get one some land and play the tune), then go back underwater and go up to King Zora's place. Give him the potion, then go out and return to the present. Go back and talk to King Zora, and he will tell you that you can enter Jabu Jabu if you help get rid of the polluted sea. He'll give you the key to the Eyeglass Library, which you can find by resurfacing in Zora Village and going to the top-right. Go in and get the book in back, then come out, play the harp and go back to the past, and go back in the Library. In back, the book will give you directions across the unseen floor to get the Fairy Powder. Once you get that, exit the Library and go left one screen. Use the Switch Hook to get across the gap, go left one more screen, and up into the Queen Fairie's cave. Give her the powder and she will cleanse the seas. Afterwards, return to King Zora, who will allow you to enter Jabu Jabu, a giant fish located in the west portion of Zora Village.
