To add to Spencer's info-
Some of the groups that have shelters also have foster programs, to decrease the number of animals that have to be euthanized. For instance, the North Texas Humane Society has a very large shelter, but still does not have enough room for all the healthy, otherwise adoptable pets. Nt only are they a non-profit animal welfare organization, they also contract with alot of the smaller Fort Worth suburbs to provide municipal animal control services, and they are also the official cruelty investigating authority for the western part of the Dallas-Fort Worth area, so even with their large facility they are short on space. (Yes, Spencer and I are neighbors!) So they accept volunteers to foster animals. NTHS will screen the potential adopters, who will adopt the animal while it's still in foster care, or take back the animal when it is ready to be adopted, for instance, a litter of babies that were weaned in foster care. There is no need to take them to the adopt-a-pets in these situations, because their adoptions are handled through the shelter. The adopters visit your home with a shelter employee/volunteer, or you can take the animal up to the shelter for a potential adopter. That way you don't have to worry about strangers coming to your house. Most of the shelters that have foster programs will handle medical care, but food is up to the foster parent.

It's a very worthwhile and noble thing to do if you have the space and time, and no pet restrictions in your lease. Let's all hear it for Spencer, and anyone else out there who fosters!