If you are going to the store, get a flea comb too. This will help you get to the places where the fleas hide - in the deepest fur and most difficult to reach places. The comb will help remove the dirt, and give you an idea of the live fleas that are lurking.

One place to comb carefully is back by the um, er, "output" places and under the tail. Also around the neck, because the kitty can't lick there.

As for catching or killing the fleas you find, one way is to wash them away under running water. Pick them up between your fingers and let the water sweep them away... Yes, this wastes water, but it also gets them away bfore they jump off your fingers and get on you or back on the kitty.

Good luck - you can expect to battle these critters for several days - don't give up!