First, treat the other animals in the house with the appropriate prescription flea meds (advantage, frontline, revolution for cats, dunno about dogs). Then, begin washing everything you can in hot water and vaccuuming daily. You can also treat carpets and upholstery with borax or food-grade diatomaceuos earth.
Then fill a little pan with soapy water, run the flea comb through each kittens fur in turn, dipping the flea comb in the soapy water, then rinsing an drying it each time.
You can also ask your vet if any prescription meds are safe on one-month old kittens. I believe the youngest is 12 weeks, but I may be wrong.
Whatever you do, do not buy OTC meds at the drugstore or pet store. The only thing any of them are good for is if you buy a flea collar to put in your vaccuum. And that's it. They are generally unsafe, by which I mean they can kill cats.