In the immediate area surrounding the exit of the tunnel is a Bottle – you can spot it easily by looking for the bubbles rising to the surface of the Lake. Dive down and retrieve the Bottle (which obviously has a note stuck inside it). Examining the Bottle reveals a letter from Princess Ruto which reads:
“Help me.
I’m waiting for you inside
Lord Jabu-Jabu’s belly.
-- Ruto
PS: Don’t tell my father!”
Taking this letter to King Zora will lead you to the next section of the game. There are quite a few things that can be done in Lake Hylia though before leaving.
Scarecrow Song
There are two Scarecrows perched on the shores of Lake Hylia. Speak to the closest one and he will identify himself as Bonooru, the scarecrow musical genius.
Use you Fairy Ocarina and Bonooru will ask you to play a tune. This can be any song that you make up consisting of 8 notes. You will have to remember this song though so keep it nice and simple.
Walk over to the Lakeside Laboratory near the shore. There is nothing that you can do inside the Laboratory at this point in the game. There a mound of soft soil located just outside the Laboratory though.
Drop a bug into the soil to reveal a 
Gold Skulltula (number 27 of 100). Take this opportunity to plant one of the Magic Beans in the soft soil as well (part of the Magic Bean side quest).
There is an island out in the middle of Lake Hylia with two pillars on it. Approach the island at night (or use the Sun’s Song to change the time of day to nighttime) to find a Gold Skulltula on the side of one of the pillars (number 28 of 100).
This is your first opportunity to explore the Fishing Pond. The pond is located on the east side of Hylia Lake – you have to swim to it in order to reach it. You can obtain a Heart Piece if you catch a 10-pound fish. Check out the Fishing Pond side quest section for more tips and tricks on how to fish.
This is everything that can be done in Lake Hylia at this point. Dive back down through the tunnel that leads back to Zora’s Domain.
