After the story sequence get out on the field and summon Epona with Epona's Song. Ride to the West and enter the Gerudo Valley area. If you speed her up enough Epona can jump over the broken bridge in the beginning of this area. If you talk to the man there (he's the boss of the carpenters, the guy you give the Poacher's Saw to in Adult Link's Trading Sequence in How To/Biggoron's Sword), he will explain that his carpenters are in the fortress. Continue on to the fortress right ahead. Let one of the guards see you and you'll be thrown in a cell. Now look up and notice the overhang of your window. Hookshot to it. Then fall down to ground level and go through the door right next to you. Follow the corridor and you'll come to a cell. Talk to the guy in the cell (the first carpenter) and you'll be attacked from behind by a Gerudo guard. I personally just Z-targeted and blocked her first attack and then wailed on her by holding forward and pushing B using Big Goron's sword. Also shooting her with arrows works well. There's probably plenty of good techniques for this fight. You have to watch out though because one of the attacks she has will knock you down and you'll end up back in your cell.
Once she's gone she'll drop a key so use it to free the first carpenter. Now continue on past the cell and go outside again. Turn left and go in the door. Turn right in at the corner of this hallway and you'll see the head of a guard poking out over a box. Shoot it with an arrow. Walk to where she was and turn to look down the next hall. From there shoot down the two guards in the next room. Go in the room (there's a Big Faerie that can be summoned using Song of Storm near the stove) and go up the ramp on the far side to an exit. When you are outside again turn right and drop down and go through the door that's there. Now just stand in the doorway with an arrow cocked and in a few seconds a guard will walk by, so shoot her. Now go right, left, right and you'll be at the second carpenter's cell. Talk to him, fight another guard, and free him.

Go back out where you came in and drop down one level. Turn left, climb up some vines, and go through the door that's straight ahead of you (NOT the one to the left). This is the third carpenter's room. Same process. Once he's rescued, go back out the door you came in. Shoot the three guards that are wandering around outside and drop down to ground level. Turn left and go into the door furthest left, the one right before the Gerudo in white clothes (Don't worry about her, she's not a guard she just lets you into the Training Center later.) Follow this hall down to the fourth and final carpenter and go through the same process to free him. Now that he's free a Gerudo will talk to you and since you are so skilled, you will get a membership card that lets you wander around the fortress all you want and participate in the activities it has to offer. Also, the bridge will now be fixed. Explore the fortress and try the various games and what not. Don't bother with the Training Ground because you can't get through it without the Silver Gauntlet.