Task 1: Escorting the Prince
Launched Up Top
You cannot visit the Lakebed Temple yet because you lack undewater gear, so use Fyer's cannon to launch up to the Flight by Fowl building. Enter the building, go down the ladder (play the minigame if you wish, but you'll have to rocket back up again), and leave through the door. Head to Castle Town.
Castle Town Tour
There are many things in Castle Town that can easily get you sidetracked. Explore for awhile if you want to, and if you haven't gotten the Hylain Shield yet, get it from the Goron Shop (southeast section of the square) on the first floor. Also, if you have a Golden Bug, give it to Agitha in the castle on the vern road for a wallet upgrade. The golden wolf awaits you outside of castle town if you've activated the howling stone in Lake Hylia.
After you are done sightseeing, go to Telma's Bar (along the second path on the left on from southern road). After a short conversation, you'll be asked if you are willing to escort the Zora Prince to Kakariko Village.
Guard the Wagon
Telma, Ilia, and the Prince need to get to Kakariko Village, and it is your job to get them there safely. The first obstacle that you'll meet is a boar-riding enemy on a bridge. While this beast is similar to the one you faced earlier after you freed Kakariko Village from twilight, the battle is much easier. When your opponent begins his charge, use the hero's bow to shoot him with an arrow. When hit, the enemy will veer towards the right, so guide your horse left to avoid a collision. Turn around and charge again. This time, your opponent will be wildly careening back and forth, so aiming will be harder. Switch to targeting mode as soon as you begin your charge for optimal aiming opportunities. After a second hit, your enemy will fall over the edge and you'll pick up a key you need to proceed.
For the next segment, you'll fend off boar-riding beasts and flying enemies as you follow the wagon to the village. Hit the archers with arrows (or your sword) before they light the wagon on fire. If they do manage to ignite it, target the wagon with the boomerang to put out the flames. Make sure you do this before the meter on the top of the screen becomes full. The flying enemies will try to toss a bomb that throws the wagon wildly off course (the wagon does correct itself eventually). Before reaching their drop point, target the winged beast with while the gale boomerang or bow is equipped and press and release to hit it, causing it to drop its bomb before it hits the wagon. Unfortunately, this task is much harder than it sounds, and will probably take several tries to keep up with the wagon and boars. Using the bow is easier to do this than the boomerang, but only possible if you have arrows.
Task 2: Going to Lakebed Temple
Zora Armor and Water Bombs
Eventually, you'll make it to Kakariko Village, where a spirit of the departed Zora Queen Rutela awaits you. She leads you into the graveyard and into an opening, to her husband's grave, where you'll receive the Zora Armor. Exit the graveyard and purchase water bombs from Barnes Bomb Shop (you may have to sell your stock of regular bombs first). If you have not done so already, the Hawkeye is available if you finish the archery contest. Head back into the graveyard and to the Zora's tomb. Go underwater (wearing Iron Boots and Zora Armor) and blast a rock in the pool using a water bomb to reveal a shortcut to Lake Hylia. Go on in.
Opening the Temple
Go to the deepest section of Lake Hylia (where the purple dot on the map is), and sink down under. If you don't have any more water bombs, buy some from the Zora near the temple entrance. Bomb the rock in front of the entrance to cause bubbles to rise. Set another bomb on the bubbles so it is carried upward and destroys the final rock blocking the entrance.
Meet Telma's Warriors (optional)
If you want to know what's going on in Telma's Bar before you head for the temple, Auru, Ashei and Shad will appear for the first time. When you chat with them, they'll think you're some civilian in a costume! The text will alter the next time you listen to them in wolf form while Midna is nearing her demise.