Right at the beginning there are boulders rolling down the path. Wait until one has passed, then run to the single pot, wait again, and run down the passageway once the boulder has passed you.
In the next room there is a Freezard and two Blue Tektites. First kill the two Tektites and then dispose of the Freezard. The path further is blocked off, but look to the right to see a well hidden crystal switch which will remove the barrier. Hit it with your bow and continue forward. This passageway has rolling boulders again - wait until one has passed then run across to the next room, you should just barely make it.
The next room appears to be empty, but jump down and you'll notice there are several Freezards here as well as a White Wolfos. You could just use one well placed Din's Fire to get rid of all of them in one go. Once all enemies are dead, the bars will disappear allowing you to continue. The next room contains a Blue Fire flame, but first kill all the Gray Wolfos that appear. Go around the left pillar to find a crystal switch which will make a treasure chest appear inside the red ice platform. Catch some Blue Fire from the nearby flame and use it here to melt the ice platform. You'll then be able to open the treasure chest which contains the Dungeon Map. Catch another bottle of Blue Fire and exit the room the way you came from.
Once back in the previous room, use the Blue Fire on the red ice blocking the path at the top. The next passageway features rolling boulders and Freezards. Run across the corridor, dispose of the Freezards, then continue, the boulders should not be an issue this time around since the passageway is very large. The next room features a path across several pillars and more Freezards. This is another room where Din's Fire will come in handy. Run along the passage, killing some Freezards on the way, to get to a treasure chest containing the Compass. Use the opportunity to catch another bottle of Blue Fire at the flame in the center, then return to the previous room.
This time, melt the red ice blocking the bottom path. The next passageway features yet more rolling boulders, so just get across. The next room features Ice Keese which can freeze you solid, so you'll definitely want to take them down first. Jump down into the room and two White Wolfos will appear, kill them or wait until they fall into the pit. There's a Blue Fire flame on the opposite side of the room, to get to it, run across and play the Song of Time to make a Temple of Time block appear. Catch some Blue Fire in a bottle, then get to the south path and use the Blue Fire to melt the red ice blocks. There are some more Ice Keese in this corridor, just run across (or kill them) to get to a door and open it.
You'll now be in a quite strange looking room. Walk forward and you'll meet the miniboss, a Stalfos. You already fought them in the Forest Temple, and the same strategies apply here - strike with your sword when he drops his guard, defend with your shield when he's about to strike. Once he's gone, a treasure chest will appear in the room, open it to get the Iron Boots. These heavy boots make you move very slowly but make you sink to the ground even in water. As soon as you collect them, Sheik will engage you and teach you the Serenade of Water.
Once that is done, the hole behind the treasure chest provides an excellent opportunity to try out the Iron Boots. Jump into the water and put on the Iron Boots, you'll promptly sink to the ground. There, open the door and walk out to return to the Tektite room. You're done in this level, so simply exit the level the way you entered it.