How do I get to Zora's Domain?

I am stuck on The Legend of Zelda: Ocarina of Time on 3DS. I am at Lake Hylia and there appears to be a temple under the lake. From what the owl said and online guides I'm supposed to play Zelda's Lullaby somewhere but I've tried loads of places all around the lake and got nothing so far.

There is an island with a stone that says "When water fills the lake, shoot for the morning sun." I have tried shooting the slingshot between the two pillars, at the sun, and playing Zelda's Lullaby there.

I'm just baffled because there is zero clues as to what to do next...

Solution 1:

The hint from the owl is to enter Zora's Domain. The entrance to the path to Zora's Domain is in Hyrule field near the entrance to Kakariko Village. Make your way to the end of the path where you will find the Triforce symbol he's referring to.

Just so you know, you can also go fishing in Lake Hylia. Also, when looking at your map subscreen the flashing dot is where to go next.

Solution 2:

Note: This dungeon cannot be entered until after you get the Master Sword and is intended to be done after the Forest Temple.

The island isn't related to the temple. It's used to get an optional item once you have the Bow.

In order to enter the Water Temple, you need the Iron Boots and Zora Tunic.

The Zora Tunic can be obtained from either King Zora or from one of the shops in the game.

The Iron Boots are located in the ice cavern near Zora's Domain.