Most kill shelters don't have great foster programs. I won't go into detail on that I would contact some rescues near you. They are always in desperate need of foster homes. Different groups have different policies. Just check out their websites and email the ones that interest you. If you don't have a particular breed rescue in mind, there are several all breed rescues. Most commonly the rescue will cover medical expenses and ask that you cover food. Some groups will cover food as well. A few of them don't cover anything. Most of my shelter fosters I end up having to pay for everything myself, but sometimes that is because I don't trust the shelter with some things.
They might do a home visit, but they might not. Everything really just depends on the individual group. I'd find one with people you like since you'll probably be sitting in on some adoption days with them. Most groups have nice people anyway. I work with a group filled with some of the most wonderful, fun people I have ever met
Good luck with fostering. I've been doing it for 6 years now and it is the most rewarding thing I've ever done. It is emotionally and physcially draining at times, but it is worth it.
Shiloh, Reece, Lolly, Skylar
and fosters Snickers, Missy, Magic, Merlin, Maya