Task 1: To the Desert
The Adventurer's Guild
Warp to Castle Town (Press to call Midna, and select "warp"). On the way into the town, you will be intercepted by the postman. Read his letter, then proceed into Telma's bar. Telma will tell you about a group of adventurers that are trying to right the wrong that has befallen Hyrule, and tells you to speak to them. They tell you that Auru has gone to Lake Hylia. Check the map to see where he is, then leave the bar.
If you howled at the stone near Sacred Grove, the golden wolf will be waiting for you south of the castle. Go to the gold dot on your map to find him. Also, stock up on whatever items you require before you leave for Lake Hylia. When you feel you are sufficiently prepared, warp to the lake and head up to the tower (it is marked on your map).
Special note: If you met Ashei, Auru and Shad before Telma introduces you, the dialogue is quite different then what you normally get after you go through the challenge to find the Master Sword. Their dialogue will show the team being apologetic for mistaking you for someone else. Glad that's over.
Bombs Links Away!
After you speak to Auru, you'll receive a memo to give to Fyer. Before you head to his cannon, go to the howling stone to prompt the wolf to enter Gerudo Desert. Luckily for you, that is where you are headed. Go to Fyer and show him the memo. he will offer you the Oasis flight and send you sky high and crashing into the desert.
Entering the desert makes Midna reflective. She tells you what happened to her people and why she needs the Mirror of Twilight.
Task 2: To Arbiter's Grounds
Restoring Eldin Bridge
A giant stone monolith is in the southeast section of the desert. Go up to it (use the clawshot to get up the mesa), and use Midna's help to return the bridge to its proper place after a bout with some shadow beings. The place where the bridge section used to lie is the now-open Cave of Ordeals. Don't head in there just yet, go up north instead.
The Enemy Camp
As you approach the campfire, shoot the bulbins from afar with hawkeye-enabled arrows. Then, mount a boar and dash through the gates to the north. Shortly after the gate, you'll find the golden wolf if you activated the Lake Hylia howling stone. Learn his move, then proceed onwards into the north.
As soon as you enter the next area, shoot the archers on the towers with hawkeye-enabled arrows. Proceed into the encampment and defeat the enemies that come your way. Shoot the tower archers to stop the onslaught of enemies, or they will just come at you forever. Defeat the creature roasting a boar to get a small key, and destroy the boar for a piece of heart. Use the key to unlock the gate at the center of the camp.
King Bulbin Showdown
The axe wielding soldier in the middle of the camp is strong, but slow. You'll be able to make quick work of him if you just keep swinging and moving. If he tends to block your frontal assaults, circle around him and attack or use the back slice. After you defeat him, the place lights on fire. Mount a boar and crash through the gates to the north to escape. Collect the poe to the east of the entrance to Arbiter's Grounds before you head in.