My fiancee actually works for the local animal shelter and city animal control and we foster cats and dogs all the time.
Fortunately (and unfortunately at the same time) it's a pretty large shelter that sees a lot of animals come through its doors every year, and so it has a lot of connections and lots of people willing to help. They temperament test every animal that comes in and those that don't pass are euthanized. It sounds cruel, I know, but for every dog that doesn't pass, there are three or four dogs that do pass and are put up for adoption. Sometimes the shelter gets so full that it can't hold al of the dogs at once, which is where the foster program comes in. Dogs that are recovering from injury or illness go to foster homes to recover while the healthy stay at the shelter to be adopted. There are rare occasions when even the foster homes will be full, and so the breed rescues help out.
Breed rescues will come and take purebred (or nearly so) dogs and cats and take care of them and adopt them to people around the country who are searching for a particular breed of animal, but don't want to adopt from a breeder when they can take in a homeless animal.
Alot of times the breed rescues are full as well though, and so there's another program called "puppy train". Basically, our shelter has a deal with a few shelters in the New England area and one in Wisconsin where people adopt many more dogs than there are strays that come into their shelters. They send someone down in a big van and take between 10 and 30 puppies every trip, and this sually happens twice or three times a month.
Last year fiancee and I fostered somwhere in the neighborhood of 70 animals. We cut back after our one of our own cats caught a rare and fatal illness from one of the foster cats, and we had to put her down. Now we only foster in life or death situations, basically where the shelter has run out of room to hold more animals and has to euthanize due to lack of space. When there are perfectly adoptable animals whose heads are on the chopping block we step in ans take them home until the shelter has space to take them back and adopt them to someone. Right now we have a silky terrier with us, who my fiancee's parents will likely adopt, as well as a mother cat and her litter of 6, who are about 16 days old right now. They were found in the parking lot of the shelter one morning, dropped off in the middle of the night in a soiled blanket. There was no space, and kittens are small so we took them in. In another 2 weeks or so the kittens will be at their cutest age (i think, anyways) when they look like kittens instead of rats, and are just starting to explore their envirnoment. I'll probably have pictures for all of you before too long.
So in reply to the OP, yes it's hard, and taxing. But someone has to do it, or there would be so many more animals that died needlessly every year. It's our way of contributing to the community, and trying to make it better.