To reduce stress for your resident dog(s) and foster/newly adopted dog(s), introduce them to one another gradually in a neutral place that neither dog has been able to claim as its own--ideally off your property. Allow your resident dog to get used to the new dog’s smell before giving it free run of your home, too, and bring the new dog into common spaces slowly. This is not, after all, a race. Taking a little time to introduce them now will lead to a calmer future for everyone, including you.
When you do introduce the dogs, don’t allow them to sniff one another nose-to-nose. (That's rude in dog language!) Instead, follow these steps:
2. Meanwhile, ask a different handler to walk the other dog around in an arc and allow the walking dog to sniff the sitting dog from behind.
3. Trade places, and complete the preceding steps for each dog.
Doesn't that sound better?
NOTE: Sometimes two handlers won’t be available. In those cases, you may want to to keep the dogs separated in different portions of your home with doors between them until you can introduce them safely.