When you get your cat from me, you should not have any flea problems for the first few weeks. Before they leave my home, I treat cats and kittens with Advantage or Frontline, flea products you get from your vet. It goes on the back of the neck where the cat can't reach to lick it off (and you have to be careful not to pet them there, as it will get all over you). Depending on the area in which you live, you may not have any flea problems at all. If you do, get one of these products from you vet. I like the Frontline (not Frontline "Plus", which has extra unnecessary ingredients) because it seems to last longer, more like 6 weeks than the 4 with the Advantage. It also lasts through a bath, and since I bathe cats for show I prefer it. Either is fine.
Another product is Program, a pill you give the cat every month. It is a growth regulator and keeps the flea from maturing properly, but it will not kill adult fleas. So if you constantly have fleas coming in, Advantage or Frontline are better. I only need to use flea control in the warmer months. Even in Southern California, there is not much flea problem (at least at my house) from November through March.
Do not use other products you can buy over the counter. Many of them are not really safe for the cats. If Advantage or Frontline are too expensive, there are some places on the internet where you can get them at lower prices than the vet's office. Don't use natural products (like flea collars) containing citrus oils either, or any product with "essential oils" on a cat. Cats absorb these oils through the skin and they are very dangerous. Even though I usually prefer to use natural products, in this case I wouldn't risk it.
Click here for a website with great prices on Frontline, Advantage and Program.