If you have a pet already and introduce a new one into your home, there are a number of steps to take. Your current pet may see the new addition as a threat and act accordingly. Should you see a scuffle going on, don't interrupt it unless there is a danger of one of the pets being hurt; this is just one animal establishing his or her place in the pack over another. But the pets should be supervised at all times if the occasional scuffle does occur.
Always keep an eye on your pets when the new first arrives. It's a good idea to keep them separate and only allow them limited interaction until they are fully adjusted to one another. This is a process that may take hours, days, weeks, and even months.
Be sure to feed, greet, and let out the resident pet before the new one. When they eat, make sure there are separate bowls in different locations, and they should always eat in those spots. If you're dealing with dogs, make sure someone is with the older dog while he or she eats, giving them an especial amount of attention.
Above all, give the pets time; don't force them together, and allow them to adjust at their own pace. And be sure to spend extra "quality time" alone with each pet during the transition period.