We have a spare room in our house that we don't use very much, so we foster kittens for the local animal shelter. When they get flooded with kittens in the Spring- Fall, we'll take in a litter or a pregnant mother and keep them for about 8-10 weeks. We provide a litter box and the food, but the shelter provides any medical care needed. Mostly, the mother cat does the hard work of raising her babies and we give her a warm, quiet, safe place to live in. They stay in the guest room full time (we keep our own cats well away). The room is uncarpeted, so if there are any little 'accidents" made by the babies, it is easily cleaned with a sponge and some hot water. Once the kittens are big enough to be spayed and put on the adoption floor, we return them. That is a little hard, because I get attached, but I know these great little ones are going to find good homes. Then we keep the mother cat for an extra week or so, so that her milk can dry up and she can put a bit of weight on, and then she goes back to the shelter as well.
We are also on a list to take in someone's cats during an emergency situation (weather emergency, someone fleeing abuse in the home, etc). Basically, if someone is in a bind and needs someone to care for their cats for just a few weeks while they get a new living situation arranged, we are available to help. Again, we would cover the food and litter costs, but since the program is run through the shelter, they will provide for all the medical needs.