Well, you run the end of the fur strip through the string about 1/4", then wrap the strip around the string. When I make a wrap, I pull the fur on the previous wrap up out of the way of the one I'm putting down. It helps to get that nice 'puff ball' effect if half the fur isn't trapped underneath the wraps.
Make your wraps snug, and fairlytight against each other. Then when you get to the end of the strip, stick that end through the string like you did on top. It'll look a little bedraggled at first, but after you shoot a few shots, the fur will poof out and it'll look fine.
Ya know, I've wrapped yarn around a few recurve strings, but never noticed it had much silencing effect. But yeah, the stuff you get at WalMart is fine. Real wool, if you can get it. Don't forget the fabric stores though. They'll have a better selection.