When you give the new dog a toy, give one to the resident. This trains the resident to have positive feelings about the new dog, since when she sees the new dog being patted or walked, she knows she will also enjoy these pleasures. If the resident dog displays any inappropriate aggressive behavior towards the newcomer, the behavior should be quickly and firmly corrected, since the dogs must learn what is acceptable and what isn't. But do not force the animals to be together if they do not get along. They may rotate their activities, sleeping, eating, and playing at different times.
Extra supervision is called for if the new dog is much smaller than the resident dog.
A large dog can easily injure a small one in play or overtire her. But, on the whole, dogs will work things out on their own, and, given a carefully chosen pair that has been properly introduced, probably become friends. With cats, many of the same principles apply. Cats are very territorial and will resent the presence of an intruder, so the trick to cat introductions is to give them the opportunity to become familiar with each other and each other's scents without giving them a chance to slug it out. Dr. Lockwood suggests having a neutral third party bring the new cat into the house in a cage.