Here is how I do it. First I size the back of the bow with TBIII and give it a day to cure out. This will ensure good adhesion when gluing the skin to the bow but also act as a vapor barrier to prevent the moisture in the skins and glue from entering the dry wood.
Soak the dried skins in warm(not hot) water while you prep the bow. I work only one limb at a time, working from the handle out the limb. When the skins are pliable roll them in a towel to remove excess water. Then add a thin but even layer of TBIII to the flesh side of the skin and a thin layer of TBIII to the back of the limb to be skinned. Lay the skin, tail towards the limb tip, on the limb and put a temporary wrap around the handle holding the skin. Work out the limb removing air and excess glue from under the skin with your fingers and be sure to center the skin as you work out the limb.
Now you wrap the skinned limb to hold the skin to the limb. I like 2" wide strips of old bed sheets. Some folks use Ace bandages. Whatever you use, it needs to breath so the moisture will dissipate. Pay attention while wrapping the limb as the skin will want to move across the limb in the direction of the wrap.
I generally remove the wrap after a few hours. At this time the skin and glue still has some moisture in them so it is easy to trim the excess skin off with a sharp blade(razor). Don't get too precise here, just the excess. You will dress the edges up after the skinning has completely cured. I use a fine file and a fine sanding block along the edges for this.
Be sure all of the scales are off of the skin before you add your finish. Lots of different methods for doing this. For a finish I use Tru-Oil. Five to 6 coats with a good buffing with 0000steel wool between each cured coat. I like the texture of the snake skin on the limb. You can get a smooth surface with extra coats of Tru-Oil. For hunting bows I give a quick spray of satin poly over the bow. It will nock out the shine of the Tru-Oil.