Tapeworms are a common problem in cats that have had fleas. Cats usually get tapeworms after eating fleas that are infected with tapeworm eggs. The felines may accidentally eat the fleas while grooming or by licking other surfaces contaminated with fleas. Getting rid of the flea problem is the first step in controlling tapeworms; but after that, you still need to clean appropriately to make sure tapeworm eggs are removed. All it takes is a few fleas swallowing leftover tapeworm eggs to pose a new tapeworm hazard for your cats.
Treat the cats for fleas before doing anything else, or reinfestation is almost certain to occur. Ask your veterinarian which flea treatment he recommends for your cat. When treating the cat, you should also treat the home for fleas. Use a vet-recommended flea spray that kills both adult fleas and eggs.
Pick up all pet bedding. Launder bedding in hot water with washing powder. Dry in your clothes dryer, if possible, or hang it to dry.
Vacuum all carpeted floors and all upholstered furniture. This removes many adult fleas and will pick up flea eggs and tapeworm segments, containing eggs, that may still be around.
Launder your own bedding, if the cat had access to it. Use hot water and detergent.
Treat the cat for fleas all year long -- use either a flea collar or a monthly topical flea medicine recommended by your veterinarian.