Use Epona to get across the bridge just before Gerudo's Valley. Have Epona to go REALLY fast and you should make it. Or, you could use the Longshot on the sign at the opposite end of the chasm bridge. When you get across you could go into the tent, but there is no need now. Walk around until a guard yells at you. They will throw you in prison. if you look up you will see some wood. use your hookshot on it. Go to the left and through the door. Now walk up the path. When you land on the lowest level, go through the door to the left. Follow the path until you get to a prison cell. Talk to the captive and then you will be attacked by a guard. Use Z-targeting and hit her when she is not blocking. 

After you kill off the guard, get the key and let the captive out. Talk to him and he will leave. Continue walking past the cell to the outside. Turn to the left and walk in the first door. Turn left and wait for a guard to show, then shoot her with your bow. Walk to her then turn left and shoot the other 2 guards. Now go to the door and walk up the ramp on the other side of the room. Go out the door. Now turn right and drop down to go in the next door. Wait there with your bow ready. 

Shoot the guard that appears. Now go through the halls in this order : Right, left, right, and you will be in another prison cell room. Talk to him then spar with the guard to get the key. Now let him out and go back where you came in to drop down a level. Turn left to climb up the vines. Go through the door straight ahead. Talk to the carpenter, and brawl with the guard, and let him out. Now go out the door you came in. With your bow, kill the 3 guards walking on the 1st level. Then jump down and head left and go through the door.