Oh boy.... skip the stress and the expense of having your cat get a bath at the vet and just take care of it yourself: launder all of your textiles that can be laundered: bathroom mats, bedsheets, petbeds and blankets and pillows that the animals come in contact with.
Take the flea collar off your pets, cut it up and put it in your vaccuum bag. The flea collars are USELESS! Go to the store and get a monthly flea treatment: we like Advantage II for our dog (they make it for cats too). It kills fleas, nymphs, larva and eggs ON CONTACT (they do not need to bite first)... which is pretty neat. Adult fleas only make up about 5% of the flea population in your home, so it's important to hit the eggs and juvenile stages!
Get a spray (at the pet store) for your carpets and upholstery: spray all areas that your pets hand out in, let it sit for a few hours, THEN vacuum EVERYTHING. Dispose of the vacuum bag in the outside trash, cut up another flea collar, place in vacuum and keep vacuuming once a day for the next week or so.
As long as you take care of it right away you should be able to get control of them. Having your pets on flea medication is an important part... they will basically walk around killing off fleas.
There are people who also treat their yards... we don't, there is so many dogs, cats and squirrels where we live it would be pointless - but with the monthly flea preventative we have yet to see a flea.
Good luck!