I said earlier that in the unlikely event that you should find a board with perfectly straight grain (where the rings on the sides do not run off to the side but continue in a straight line for the whole length) that you don't necessarily have to back your bow. But if you're making a bow for the first time, I think you should back it anyway. It's better to back it and not need to than to need to and not back it. You don't want to break your first bow.
The purpose of a backing is to create one continuous smooth surface on the back of the bow. You see, the back of the bow will be under tension. If you have run-offs in the grain, a splinter could easily lift there. Once a splinter begins to lift, it creates a weak spot, and the bow will surely break. The backing prevents any splinters from lifting.
There are plenty of other backings you could use (e.g. silk, linen, etc.) that you can get for pretty cheap, but I'm going to use sheetrock tape (otherwise known as drywall tape) and wood glue.
There are some advantages and disadvantages to using sheetrock tape.
1. It's dirt cheap. You can back several bows with one roll.
2. It's readily available. You can get it at just about any hardware store like Lowes, Home Depot, or whatever. (It doesn't matter what colour you get, by the way.)
3. It's very easy to apply.
1. It's made of fiberglass. If you use a file or a belt sander to trim the edges, you can get fiberglass splinters that will cause the itchies.
2. It uses a lot of glue.
3. It's kind of ugly.
Okay, the first thing you should do is lay your bow down with the back facing up (See? This tutorial is idiot proof!). Try to lay it down on a level surface, because the glue will drift to one side if you don't. I lay it down on a pine board I got out of a construction site dump. This way, I don't mind if any glue drips on it. I put smaller pieces of pine under the ends since the handle in the middle would cause it to "see saw" otherwise.
Then you need to measure out three pieces of sheetrock tape just a little longer than the bow. It's sticky on one side, so I just stick a piece on the back of the bow, cut it off, unstick it and set it aside. Then I do the next piece, and then the third.
Next, squeeze a healthy stream of glue all along the back.
Don't be stingy with the glue. Once you have that stream of glue, spread it across the width of the bow with your finger. Make sure you cover the whole surface. Then take one strip of the sheetrock tape, start at one end of the bow and begin laying it down on the back. Once you get it on, start at the handle and, using your finger, smooth it down to the tips. The glue should saturate the mesh and look something like this:
If you don't have enough glue, add a little more until you do. Then next time you'll have a better idea of how much you should put on there in the first place. Be sure there are no places where the sheetrock tape buckles or warps or anything.
Let that sit for about 10 or 20 minutes--enough to create a slight film--and then add your second layer. Use a stream of glue, spread it, apply the backing, and smooth it down. Let that sit for another 10 or 20 minutes, and then apply the third layer. Once you've got it all on, let it dry at least 24 hours. Here's what it looks like when it's dry.
Now ya gotta trim the edges. You can do that with the surform, an exacto knife, or a box cutter, but it's much easier with that handy dandy four-way file/rasp I showed you earlier. You might want to wear gloves, though. That'll keep your hands from itching from all the fiberglass. Don't be afraid to take a little wood off with the tape. You don't want to have a sharp corner anyway. Having the edge radiused will help prevent splinters from lifting. Once you get it all trimmed and stuff, sand the corners. Here's a final look-see.