In reply to squarepeg:
My dog had fleas last year.
The first thing to do, is to read up on the 'flea cycle'. Once you know how that works, the easier it will be for you to know how to deal with the problem.
Next, get the cat on a proper flea program and keep doing it.
That's the easy bit...
Wash everything that the cat has been in contact with that you possibly can and even better, dry all those items in a tumble dryer.
Ideally, do not return those items to the house until you've done the next stage and if you do, seal them in bin liners, etc.
Hoover everything you possibly can, especially towards ground level and where the cat has access to. Empty the hoover as soon as possible.
Now you're ready for Insect Armageddon.
Spray anything that is remotely textile and don't spare the spray! Sprinkle powder in the bottom of cupboards, along the skirting boards and under the bed, etc. Please note, cats and dogs have different fleas and different insecticides accordingly. I know the stuff for dogs is poisonous to cats, not sure if the cat stuff is poisonous to other pets, etc. (think fish will need to be removed during the spraying process).
At the end of my de-fleaing process, there was dead insects everywhere and the place smelt like an industrial plant. Think they must have left their various cubby holes in a vain attempt to escape...
Good luck!