This article is from the Your New Dog FAQ, by Cindy Tittle Moore with numerous contributions by others.
Select a dog that is, to the best of your knowledge, accustomed to
other dogs (i.e., one that is socialized with other dogs). Also, pick
the opposite sex dog than the one you currently have, if possible.
Hopefully, you know your current dog well enough to know how well it
gets along with other dogs. If it is a naturally submissive dog when
around other dogs, it probably does not matter too much whether the
adoptee tends toward submissive or dominant (but not _too_ dominant).
However, if your current dog is a dominant dog, a dog that has been
around you for a long time, or a male dog (generally speaking), your
best bet is a dog that tends towards the submissive and is _smaller_
than your current dog (like a small, quiet, female). Size is can be
important as your established dog may feel threatened by a newcomer
that is larger than he or she.
Introduce your established dog and the new addition in a neutral
place, like a park or a home that is new to both animals. Both dogs
should be on a leash. If your current dog is obediance trained, a
down/stay is in order. Allow them to sniff one another and encourage
play, discourage agression. Should your adoptee show agression,
forcibly place the dog in a submissive posture and hold it there (as
in an alpha roll). Then allow your established dog to come and sniff
the new dog. What this does is diffuse a potentially violent situation
by forcing the new dog to be submissive to your established dog. The
new dog learns to trust the established dog by realizing that the
established dog is not going to eat him, and your established dog
learns that the new dog is submissive to him. This fosters trust
amongst the two animals. This may not be necessary, but sometimes it
is. By all means, if the dogs want to play, _let them_. In fact,
encourage them, and don't interfere unless you feel you must.
At home, the first thing you must do is establish a spot for each dog
that is physically separated from each other. Kennels, crates, or even
different rooms. Never, never, never feed the dogs together. _always_
feed the dogs simultaneously in these physically seperated areas (if
in different rooms, close the doors while the dogs eat). If you must
free-feed, the dogs should be placed in their respective areas for the
entire time each one's food is down. Also use these areas for
"time-outs" when the dogs are misbehaving.
The second thing that is required is that you must be sure to spend
quality time with your established dog, and just with him. You may
even need to increase the frequency of normal activities you would do
with your established dog. This helps keep your established dog from
feeling misplaced by the newcomer.
Finally, be sure and do activities with both dogs. This encourages the
dogs to do fun things together, as well as fostering pack cohesion and
Remember, the general rule of thumb is to make sure that both dogs
realize you are alpha. They will need to work out their own hierarchy
among themselves, but they must understand that you are on top and you
are in charge.
With cats, you should make one room be cat accessible only. The
easiest way to do this is to put up a barrier in the doorway. As long
as your dog does not want to kill the cat(s), they will eventually
adjust. Make it very clear to your dog that it is not to chase cats --
correct it for even looking at the cat -- and things should work out.
Keep in mind that cats can take up to six months to adjust to a new
dog, even a friendly one. Patience.