I had a bad flea infestation after taking in a stray puppy for all of 1 day before I got it to a rescue. I went from noticing one flea to noticing a couple to seeing them everywhere in a manner of days, about a month after the puppy left us our present. It was a pain in the ass and made me hyper paranoid, so I learned how to handle it the proper way.
I agree with what others have said as a first step: Flea Bath and/or nitenpyram to remove the fleas on the kitty, flea preventative to keep them off. Wash all the fabrics and surfaces, especially near your cat's hangout spots, and dry on high heat.
Vacuuming daily is a triple threat at reducing the numbers: Sucks up the eggs/larvare/pupae/adults, the vibration and warmth tricks pupae to emerge (they can be dormant for up to 6 months and their shell acts like velcro, making them hard to remove) which speeds up the cycle and reduces the risk of reinfestation, and cleans up the grime that the larvae feed on before pupating. Just make sure you use a bagged vacuum or seal the vacuum waste somehow before tossing it. If the infestation is minor, keeping up to date on the preventative and regular vacuuming should be enough.
If you find more, especially down the road a few months, it probably means an infestation started under your nose. If you can afford it, a pest control pro is the best solution. If you can't, the best flea killer spray for whole home infestations is Precor 2625. It is a whole home premise spray that kills the fleas at all stages, both on contact and by disrupting their reproductive cycle. You'll want to either kennel your kitty for a day to apply it, as the contact kill chemical can make cats sick, or at the very least quarantine them and do the spray over a couple days away from them. Get a coverall suit, N95 mask, and spray all low surfaces, all fabrics that can't be dried on high heat, under couch cushions, all corners and crevices around the floor and your bed, literally everywhere below knee height and anywhere your cat might like to climb or hide.
The preventative is supposed to last 7 months, slightly longer than the longest normal pupae duration, so that multiple flea generations will be affected. I do recommend a second spray 1 month later, just to be safe, and continue daily vacuuming over the entire premise for at least that first month to expedite the lifecycle as much as possible.