In Gerudo Desert, Mutoh needs help finding his carpenters, who are supposed to fix the broken bridge.
Make sure that you have plenty of arrows. You can buy more in Kakariko Village.
Go to Gerudo Valley, which you can reach in the west side of Hyrule Field.
You can cross the broken bridge with the Longshot, or Epona can jump across.
Use Sun's Song to turn it into night, then kill the Gold Skulltula behind the tent, and kill the Gold Skulltula on the rock arch.
If you talk to the carpenter, he asks if you can rescue his carpenters.
At night, go west to Gerudo Fortress.
Enter Gerudo Fortress
If any of the Gerudo guards sees you, you get thrown in jail. You can use your Longshot on the wood above the window to escape the jail cell.
If you want to avoid jail, go past the stairs and carefully walk up the slope, watching for a Gerudo guard to the right. Don't let her see you. Stand in a position so you can shoot her with an arrow without her seeing you. This will only stun her. Then go through the nearby door into the fortress. It's the door farthest to the left.
(If you got thrown in jail, drop down from the window and go through the first door on the left.)
Rescue the First Carpenter
Inside, talk to the carpenter through the bars. A Gerudo drops from the ceiling and attacks. Turn around and target her.
Switch to the Master Sword if you were using Biggoron's sword. That way, you can use your shield. If the Gerudo hits you too many times, you will get thrown in jail, but the shield helps prevent that. When she crouches, move to the side, then after she does a jump attack, hit her with your sword.
After you defeat her, she jumps into the ceiling and leaves a small key. Open the jail cell and talk to the carpenter, Ichiro, to free him.
Rescue the Second Carpenter
From here, go through the exit near the cell that has a skull over it.
Quickly go through the door on the left. Inside, go to the right, and watch for a Gerudo guard to stop by the crate at the far end of the hall. Shoot her or wait for her to go back, then go through the exit on the right.
Outside, carefully go straight ahead, but look for the Gerudo guard on the ledge to the left. Shoot her from around the corner. Then jump up onto the ledge and go through the door here. There is another cell straight ahead. Talk to the carpenter to make another Gerudo attack. Defeat her as before and get the key, use it on the cell and talk to the carpenter, Jiro, to free him.
Rescue the Third Carpenter
Exit through the passage to the right of the cells.
Climb down the vines ahead, and go through the door straight ahead. Talk to the carpenter, Sabooru, and fight the guard to free him, then go to the right from the cell to exit the way you came in.
Get a Gold Skulltula
Go back up the vines and go through the door on the left. There are guards in the room down below, so stay where you are. You can shoot one with an arrow from where you are standing. Then walk a little bit farther ahead to shoot the other. Go up the far ramp to the outside.
Go to the corner of the ledge that you are on, then use the Longshot to get the Gold Skulltula on the wall (if it's night time).
Free the Fourth Carpenter
Jump down to the right from the door, and go through the door down below. Stay still, then shoot the guard who walks by. Go to the right and free the carpenter, Shiro, as you have done before.
Become a Gerudo Clan Member
A Gerudo will tell you that they are impressed that you got past all the guards, so she gives you membership in the Gerudo clan. Once you have your membership card, you can stroll through the fortress without getting thrown in jail.
Get New Items
Before continuing, take Epona to the archery range behind the fortress. If it's night, there will be a gold skulltula on the far tall target. If it's daytime, you can play the archery game. The prize for the first win is a piece of heart, and the prize for the second win is the biggest quiver.
Before you leave, get the piece of heart in the chest on the roof of the fortress. You can go into the fortress and make your way to the roof, playing Scarecrow's Song up there to reach the chest, or you can use the Longshot to reach the windowsill of the jail cell, jump down onto the fortress, and go inside to reach the area above the jail cell.
You can go to the Gerudo Training Ground to get the Ice Arrows if you wish.