Get on the ledge above the gate. You want to stand near the left side the a square pattern on the ground. Go into C up and align the left side of the B button with the right side of the closest entrance (the angle is not precise at all so you don't have to line it up perfectly). Sidehop and jumpslash over the gate and you should enter it. This works as both child and adult.
Head up to the path that leads to the horse archery game located on the left side of the fortress. On the right side at the end of this path is a seam that you can use to walk up the cliff if you angle yourself correctly. A very easy way of scaling this seam is to activate ISG so that you cannot fall off the seam's narrow ledge. If you do not wish to use ISG, you can use C-up to angle yourself properly to climb the seam. Once you have gotten up the cliff, walk over to the top of the entrance you previously took to get here. Get as close to the edge and ceiling as you possibly can. Now align yourself so that you are perpendicular to the ceiling. Sidehop, and if you positioned yourself properly, you should stick to the ceiling and glide back down to the fortress which is now unloaded. From here, navigate your way into the training grounds. Note, to get into the fortress as a child you will have to use Cucco Jump.
The set up with the above trick as child on the seam and anti-gravity works the exact same way as adult; however, it is required to get past the gerudo guards to get up here in the first place. There are two ways of doing this.
First, steal the rod and then become swordless. Call Epona and ride her to Gerudo Fortress. Then perform the RC Epona Glitch, and move her past the top white gerudo. After she is past, climb back on. The upper portion may be unloaded, so move back towards the fortress a bit, then come back up to load the upper area. Then perform the seam walk and anti gravity trick as described above.
For this method, stand on the platform high above the last white guard you need to pass. From here, angle yourself so that a hoverslide will go up the slope. The angle here is not very precise, but the next part is important. You must perform an Inverse Camera Angle, but do it so that the camera is on Link's left side. From here, perform a superslide and then pause and equip the hover boots. If done correctly, the guard will not catch you and you can enter the upper fortress area. Then perform the seam walk and anti gravity trick as described above.
It is important to note that this trick can only be done as Child Link. Once you have entered the training grounds, head into the room where the ice arrow chest is located. Climb part way up the grate, and then use a bombchu to vine clip to the ice arrow chest. From here, you can either savewarp out, or use another bombchu vine clip. Note that it is also possible to clip with a bomb explosion.
In the room with fire keese, torch slugs, and a fire ring in the middle, it is possible to get the key without hammering any of the blocks. Simply allow a torch slug, fire keese, or the fire ring itself to damage you, then roll into the chest and press A. If done correctly, you will open the chest and obtain the key. Note that with vine clipping as a child and this trick, it is possible to get up to 6 unused keys as a child.
Using a weirdshot, you can bypass the Song of Time blocks that prevent you from accessing the underwater section of the room.