How do I get rid of fleas!?

My boyfriend's cats have fleas and his family haven't been giving them proper treatment to get rid of them (the poor things). As a result the fleas have moved from his house to mine. They're biting us to pieces and it's driving me crazy! How can I get rid of them without having to wash all my clothes, bedsheets and carpet? Do I have to call pest control? Is there a product I can use?

I do own a cat but he's been treated against fleas and doesn't seem to have any. If they only live on animals then how on Earth are they surviving?