If you are planning to introduce a new pet into your household that already has a pet(s) then there are a few things that you can do to make the introduction and integration process a lot smoother and stress free for both you and your pets. It is advisable to pick a new pet that is younger, smaller and of the opposite sex than the already established pet as the older pet will feel less threatened, giving the newcomer a better chance of being accepted.
When introducing the animals it is best that they are supervised at all times, especially if the new pet is very young as a resident cat can accidentally scratch a playful pup or an older dog could easily hurt a new kitten. It also helps if the animals are spayed/neutered.
If you are trying to introduce a dog to a dog then perhaps think about letting them meet for the first time in a public park or somewhere out of the house so that the older dog regards the new pet as a potential friend, rather than an intruder. To enhance the experience have someone else take the new dog and wait until they have started to play and be comfortable around each other before taking them both home. When you do get home make sure to give the resident lots of fuss and attention and play down the presence of the new pet.
Cats are very territorial and will not like the introduction of another cat. It can help to give them a chance to get used to each other’s scent. A good way of doing this can be for the newcomer to be brought in to the home in a pet box and leave it where the resident can come up and investigate and smell the new animal for about an hour. Once they have had a good sniff, let the new pet out and be sure to keep an eye on any inevitable hissing, spitting or fighting; this is only natural but be sure to break it up if it looks like a serious injury could occur.