What is the most thorough way to get rid of fleas in the house?

If they are bad you need to bomb your house. The ones in the stores are garbage, order from a veterinary supply place or you local vet. It calls for removing you and pets out of the house for several hours. Covering pillows, bedding and ANY food stuff. A monumental task. The bombs are spray cans you put in each area sit on the floor, lock the sprayer out and let them spray all contents into the air. You have to set and run out of the room!!!!

The tiny flea eggs are like grains of salt and roll into floor cracks carpets etc. No amount of vacuuming will do the trick to get rid of them. for YOUR sake and YOUR cat(s) get frontline or interceptor for your pet. They are miserable with fleas and fleas can carry a multitude of diseases including tapeworm. If you don't treat your house if there is an infestation that is why you can't get rid of them totally. The meds should work well on you pet and some prevent eggs from hatching while others kill adult fleas. If you are using flea products you buy in the stores you are wasting your money.

Some tips here may help: https://www.craftylittlegnome.com/kill-fleas-in-the-yard/

de flea your cat by bathing using Dawn dishwashing liquid. The original Dawn that has the ducklings on label. It may take a few baths but the fleas will be gone. This will kill the flea egg too. In the home there is an old wives tale that using "horse apples" in the home or out in the yard will keep fleas away. Split them in half and place in various corners of your rooms away from children (don't know about pets). "Horse apples" grow on Bois d' Arc trees.

https://thebugskiller.com/how-to-kill-fleas-and-get-rid-of-them-forever-from-your-house-dogs-cats/

You need to treat the house and yard as well as your pets.

Capstar is a great way to kill adult fleas on your cat and you can safely give it everyday until they are gone. I would get a growth inhibitor, one that mixes with water (Martin's comes to mind), and treat the house with that. Vacuum each and every nook and cranny, then treat. It will not allow eggs or larva to develop into adult fleas. It's much safer for you and your pet to avoid the harsh chemicals that come with foggers and sprays. If your cat is indoor/outdoor, once you have the situation under control, look into Advantage II and don't skip a month. I think treating the yard is futile, other animals deposit eggs when they encroach. Protect the cat or you could make him/her strictly indoors.

Treating your yard is crazy. Rabbits, chipmunks, squirrels, groundhogs, mice and moles run thru your yard continuously and ALL of them carry fleas. The rain washes the stuff you use and the dew washes it off of the grass nightly. I wouldn't waste the money on it. Treat the house, treat the pet.