Backing a bow (adding a layer of another material to the back of a bow) is done with a variety of materials for a variety of reasons. Some backings change the properties of a bow (wood, rawhide, etc.) and some are just for looks and to add slight protection from splinters lifting on the back (snakeskin, paper, etc.). In this post I'll explain how I applied a paper backing to my bow. I'm by no means an expert, but my method seemed to work very well.
I backed my bow after gluing on the handle and tip overlays, but before I did anything else. I figured if a splinter was going to lift it might happen during tillering, so it makes sense to back it ahead of time.
I'd recommend laying everything out on a clean work surface to make things go smoothly. Cut the paper roughly to size and lay it out beside the bow. You'll also need to water down some wood glue in order to make it easier to spread across the back of the bow.
Start by putting a good coat of glue on the back of the bow using a brush. Then carefully place the paper over the bow, and work from one end to the other to smooth it out. It is good to have a helper for this, because lining up a 6' piece of paper by yourself is tough.
Using a rolling pin is very effective for smoothing out the backing and ensuring that it is tightly pressed against the back of the bow.
Right after applying the first piece of paper, repeat the process with a second piece of paper. Then let it dry. Once dry, use a file on the edges to remove the excess paper.
After this I rounded the corners of the bow, removing more of the paper backing in the process. This is okay because a splinter is unlikely to lift in the rounded section, so the paper isn't needed there. I think it also looks good to have the paper stop and not wrap around the edges. In addition, it leaves a very clean edge to the paper, and makes it difficult for the paper to peel off.
Around the tips I left lots of excess, and then sanded away the paper to about a 1/2" from the tip overlays.
With an oil finish the paper really darkens and stands out against a light coloured bow.
All in all I am very happy with how this turned out!