Now that the Master Sword lifted the twilight curse from you, you can turn into a wolf whenever you want to and thanks to this, warp to almost anywhere! After Midna tells you about the Mirror of Twilight, use this new ability, talk to Midna and ask her to warp you to Hyrule Castle Town. Turn back into your human form, then get in the city. Read the letter you got from Telma.
Hyrule Castle Town
Go back to the tavern and talk to Telma. Then speak with each member of the band to learn about Snowpeak and Gerudo Desert, check the map on the table, then leave the tavern. Get to the southern street and enter Agitha's Castle. Talk to the little girl and if you've already found insects, talk to her once more to give them to her. As a reward, she will give you the Big Wallet. Get out of town from the south, go down all three stairs, then go left and get close to the shiny wolf. You will be taught the Helm Splitter.
You can also warp to Kakariko to help the Gorons' shop. Get back to Malo Mart, talk to the Goron Elder Gor Liggs who will tell you about a donation, then get in the shop (daytime) and make a donation to the Goron Elder Gor Ebizo to build a bridge. Don't forget to come back later to give him more rupees, for example after giving insects to princess Agitha. Then warp to Lake Hylia.
Head south, climb the ladder, and then head east. Climb the ladder to the top of the watchtower, where Auru is waiting for you. He tells you about the Gerudo Desert and a cursed mirror, then he gives you Auru's Memo for Fyer. Come back down and head towards the Howling Stone near the lake's bank, not far from where you stand. Turn into a wolf, howl the melody twice and a new symbol will appear on the mini-map. Come back to the house in the middle of the Lake. Show Auru's Memo to Fyer to earn a free "Oasis flight"!
Once you arrive in the desert, Midna tells you what happened to the people who tried to use the magic of the Fused Shadows. They were sent to the Twilight Realm by the goddesses from where no one ever returned. This is the story of the Twili, of which Midna is a descendant. The Zant took control of it and transformed all of the Twili into shadow beasts. The Mirror of Twilight is a link between the two worlds and a path to the Twilight Realm.
Next, head northeast. When the boar-riding guards attack you, shoot arrows at them, then get close to a boar without any jockey and ride it. Go towards the two towers in the far north with a barrier between them, then speed up your boar to destroy the two barriers. Keep on going by foot, go north and you will meet your wolf friend again. This time he will teach you the Mortal Draw. After that, go left.
Go ahead, climb the central stairs, walk around and head northwest of this area. There attack the enemies until one of them drops a key. Pick it up, then go to the middle of this place, in a passage with a fence on the north and south sides. One of those fences has a lock, unlock it with the key you looted earlier, push the door and get in. Attack the monster with some jump attacks and back slices, then after he leaves and puts the place on fire, ride the boar, go south, face north, align with the gate you went through and dash to destroy the barriers that block your way.
Next, get off, climb the stairs, go left, shake your Lantern next to the two torches and pick up 50 rupees in the chest. Then go right, turn into a wolf, pick up the Poe's Soul, then come back to your human form. Take the stairs down to the...