We had to deal with a flea infestation last year. I think they came in on our dog since the cat was indoor-only.
As others have noted, Advantage was not killing the fleas. I spoke to our vet who recommended one of the new treatments. We washed both animals, re-treated them. I kept the cat in the bathroom for a few days, brushed her daily and picked up a lot of dead fleas.
All of the bedding got washed on hot including dog beds, blankets from her crate, etc. Cat furniture was moved to the garage and sprayed with a flea killer from the pet store and it stayed out there for a couple of weeks. Stuff that might have had fleas/eggs but which couldn’t be washed was sealed in plastic garbage bags and kept that way for a couple of weeks (it takes the eggs several weeks to hatch, you have to keep killing or ensuring there is no food supply long enough to get current fleas as well as the next generation of eggs).
Plan on having to wash everything - all your linens, towels, clothes.
Vacuumed the whole house multiple times with a HEPA bag in the vacuum - cleaning up hardwood floors is simple but carpets took a lot of going over.
I also dusted the carpets with diatomaceous earth (get the stuff specifically intended for killing insects, not the pool supply variety). Sprinkle a little on the carpet, brush it in, let it sit for a while and then vacuum up. Note that a little bit of DE goes a long way and that you really want to use a HEPA vac to suck it up. Wear a dust mask and open the windows because no matter what you will get dust all over the place. Wipe down non-porous surfaces afterwards (I just used a damp rag, to get the dust that settled on the TV and furniture and whatnot).
Seal the vacuum bag in a plastic garbage bag and toss it in the trash outside right away. You don’t want fleas and/or eggs in the vacuum to get back into the house.
You’re in the home stretch. Continue vacuuming every couple of days (it may take a few tries to dislodge all the bugs/eggs, and there will be a few more hatching over the next couple of weeks as noted above) and disposing of the bags as before.
I used the same flea-killing spray to hit hard-to-reach areas such as carpeting under the sofa, mattresses and the like. Read and follow the directions - there are safe ways to use the stuff around pets and babies.
Finally, if you’ve got a yard, keep the lawn mowed, trim plants to minimize shade (outdoor fleas seek the shade) and you may want to apply a spray-on flea killer designed for yards. I got a bottle of the stuff that snaps onto the garden hose.
Good luck!
It took a while and some work but we haven’t had a flea problem since.