You need to complete the Ice Cavern before going to the Water Temple. As an adult, go to Zora's Fountain. Where Jabu-Jabu used to be is a large block of ice. Climb onto it. From the high end you can jump onto a round block of ice. Jump toward the right where there is a piece of heart waiting for you on an ice block. Then jump from block to block in the other direction, into the cave entrance across the fountain.
You can either do this the quick way, or the not-so-quick way. The quick way is to go straight to the back of the cavern (it's pretty much a straight shot; follow the instructions below if you need help) and catch some blue fire in an empty bottle, then go back to King Zora and use the blue fire on him. The not-so-quick way is to clear this whole mini-dungeon. You don't need any extra items to clear the whole thing, so you may as well do it now. It's up to you.
For the long way, follow the path until you get to the big room with the spinning razor trap. Carefully kill the freezzards, then run through where the bars were.
Follow the path here until you get to a room with a spinning blade in the center. You need to collect all five silver rupees to open the way. Avoid the blade and get the silver rupee near the center, then quickly follow behind the blade and collect the next two rupees the same way. Then cut the icicles down near where you entered to get the fourth rupee. While in this area, use the hookshot to snag the gold skulltula. Finally, get up on the ledge where the exit is, and jump from it to get the last rupee. The door will open, so climb up and go through.
Follow the path to the next room, killing the freezzard on the way. In here, first you want to take out the ice keese with the hookshot. The easiest way is to get close enough that it starts heading for you so you can target it. Try not to let it hit you, or you will be frozen. If you're frozen, tap all the buttons to escape. Climb up onto the ledge, wait for the freezzard to stop blowing cold air, and hack it to pieces. Then jump to the platform with the blue flame. Empty out a bottle (you won't need the bottled bug for a while, so you might as well get rid of it) and catch some blue fire. Then wait for the next freezzard to stop blowing cold air and hack it to death, then walk over to the chest frozen in red ice. Melt it with the blue fire and open it, then jump back to the blue fire platform and catch some more.
Go back to the room with the spinning blade. There are red ice walls to the left and right, walk up to the one to the left and melt it. Go through and follow the path to the next room.
There are a lot of falling icicles in here, so don't stand still too long. First run straight across, cut down the icicles, kill the keese with the hookshot, and catch some blue fire. Now go to either side of the room where there are icicles to cut down. Kill any keese and melt the red ice. On one side of the room is a piece of heart and a gold skulltula, on the other side is a chest containing the compass. Before leaving this room, catch some more blue fire, then leave.
In the room with the spinning blade, go straight across and melt the red ice, then follow the path to the next room. Get rid of all the ice keese in here, then get the gold skulltula on the wall left from the entrance. Be careful not to fall off the edge.
Next push the ice block in the direction away from where you entered. When it hits the ice, push it left. When it hits the next bit of ice, push it right, then left, then right, and it will hit the wall just below a blue fire spout, so climb up and catch some blue fire. Now push the ice block off the edge so that a new ice block rises up from the ground where you found the first one.
Push this one away from the entrance like before, but this time when it hits the ice, push it right. It will end up below a ledge with a silver rupee encased in red ice. Melt the ice and collect the rupee. Jump back down and push the ice block off the edge to create a new ice block.
With your back facing the way you entered, push this one left so it hits the ice. Climb up and collect the silver rupee, then carefully drop back down (you don't want to fall off the edge). Push the ice block right, climb up and collect the silver rupee, and before going back down, jump to the ledge with the blue fire and catch some. Then push the ice right, climb up and collect the rupee. Push the ice right again and collect the rupee, then push the ice right one more time and it will stop just below the exit. Climb up and leave.
Kill the freezzards on the way. At the end of the path, melt the ice and go through the door. Walk further into the room to fight a white wolfos. Kill it as you did the wolfos in the Lost Woods. Open the chest that appears for the iron boots, then Sheik shows up. Learn the Serenade of Water from him (don't play it yet; it transports you to Lake Hylia), then walk to the pool of water behind the chest. Equip the iron boots and jump in. At the bottom, open the door and follow the path out of the water. You'll end up in the second room of the dungeon.
Instead of exiting the cave, first you want to go left from where you end up. When you arrive in the spinning blade room, make a right and catch some blue fire. Now you can exit the cave and go back to King Zora. When you thaw him out using the blue fire, he will give you the Zora Tunic in thanks. This tunic allows you to breathe underwater.