This is a really great book, my randomized algorithms class last year reference it last year. The main way you want to use these techniques is to show that a simple algorithm fueled by some bit supply of randomness (at least at the first time step to initialize some protocol variable) will then at some point in time hit a ``good'' state with high probability, and then you want to show that this convergence happens very quickly. Off the top of my head, i can't think of any slick examples, but if you want to do clever algorithmic hacking, this is the sort of math to know!