I foster! Er, I should say I have failed Fostering 101 countless times!

The rescue I am with tells us to make OUR pets a priority. Keep their vaccines up to date, and make sure they are safe and content when a newbie arrives.

With cats, do the same thing as if introducing a new cat: go slow, keep the foster apart in a room with the door closed for several days. There are several threads on this, if you need them I can try and pull them up for you.

With dogs, I am with a breed rescue. Bichons have low prey drive, so introductions are usually easy. Still, there are steps:
- keep all on a leash
- try and have them meet out in the street first, or in the fenced in back yard
- then I keep mine outside while I let the foster in the house to roam, learn the layout, find the water bowl.
- let the foster back out with the others.
Only after all THAT do I let them all in the house together.

Is this the kind of thing you meant?
If you have more specific questions, ask!