dilemma

I would like to bring home a cat that needs a home from the humane society. How do I do that without getting the rest of my cats sick?

I don't know if you're referring to illnesses that are contageous but most reputable shelters and rescues check for the big ones like leukemia and FIV. That's what makes the FIV vaccine so bad it causes a positive result on the quick test for the disease so the cat would be put down. As far as stress from introductions there are several threads that will tell you how to do it. Mostly it involves switching things with scents on them and taking it real slow.

I would hope that the shelter has already tested for the nasties and the kitty is negative (Feline Leukemia and all that) and I would hope that they have dewormed and treated for fleas prior to adoption.  To keep your other kitties from getting sick, be sure to isolate the newbie in a room (spare bedroom or bathroom) with all the amenities (litter, food, bedding, water, toys).  Get the kitty to your vet for a wellness check as soon as possible.  Allow the kitty a few days to calm down and get used to being in your home and to become familiar with you, then start introducing the newbie to your other kitties using the guide in the behavior forum.