I think that the suggestions for taking the cat to a groomer for the bath is the best idea, and the groomer can also use a flea shampoo to be sure that all of the fleas are killed.
You can also get one of the flea preventions mentioned, and start using it on the cat. Also get something for the dog; since if one of them has fleas, it is totally likely that both of them have fleas. The fleas will be in your carpets, and also in the pet's beds; so you will need to treat those areas as well. You can sprinkle some of the vacuum-up flea killer, or you can also use either borax (laundry additive) or diatomaceous earth, both of which will also kill fleas.
You can also add the Diatomaceous earth to your pet's food, and it will kill any parasites that they have, such as tapeworms. DE is harmless to people and pets, and is in fact a good source of trace minerals for them. It looks like flour, and can just be mixed in a little bit of canned pet food.
