Once you bring your new pet home, it's a good idea to take him or her to your vet for a check-up. It will give your vet a chance to get acquainted with the pet and make sure that he or she is in good health. It also will provide a baseline to refer back to as your pet ages. It's also a good idea to provide your new pet with a collar with identifying tags. A newly arrived pet is more likely to wander off or get lost than one who knows where home is. Finally, it's very important to give your pet, and yourself, a break-in period. You are both getting used to a new situation, and you shouldn't make judgements about how the adoption is going to work out in the first few days. This is especially true if you are introducing a new pet to pets you already have. It usually takes one to two weeks for dogs or cats to adjust to each other and figure out their places in an expanded family.
You can make things easier with these helpful tips
If your introductions become violent to the point that you think someone may become injured, don't worry about the steps below. Separate the animals and use your judgement as to whether to re-introduce them later. Use great caution in dealing with fighting animals. In the heat of battle, even the most loving pet will bite first and ask questions later.
Don't force your pets to interact. Letting them get used to each other on their own pace is less stressful.
Don't lavish all your attention on the new pet. It's easy to pay more attention to the new baby, but greeting a newcomer is hard enough on an established pet without feeling like s/he's being replaced. Give everyone lots of love and affection.
Make sure the new pet has a separate food dish and his or her own toys. Again, make sure your other pet(s) know they are not competing with the new one.
Don't punish the animals if they hiss, growl, or swat at each other. This is normal and part of the getting acquainted process. Do praise them if they behave well.
Give senior-citizen pets a little extra time to get used to the changes. They are not as open to change as young animals and may be intimidated by the energy of a younger pet. If you are introducing a puppy or kitten to older animals, don't let the older pet become a plaything for the youngster. What is play for a puppy or kitten can be painful, frightening, or just plain annoying for an animal without the energy to respond. Make sure that youngsters have plenty of other things to play with. If the younger animal repeatedly pesters the older, you can block off a portion of the house or yard to be "adults only."