If you are bringing your new cat into a home with other cats, keep in mind that there are diseases and parasites that cats can transmit to each other, and some of these are fatal. There are also certain parasites such as roundworms, that people can get from cats. Roundworm eggs are passed in the stool and are so small they cannot be seen without a microscope. Roundworms are especially a concern for young children, who often put their fingers into their mouths after playing with pets. Before you bring a new cat into your household, take it to your veterinarian for an examination and stool sample check. Your veterinarian will be able to tell you what vaccinations your cat needs and check your cat's stool for intestinal parasites. Your veterinarian can also perform blood testing for feline leukemia virus (FeLV) and feline immunodeficiency virus (FIV). Then you can bring your new cat home without concerns about compromising the health of other cats or people in your household.
Keeping the new cat in a quiet, separate room is especially important if there are other cats in the house. The other cats will quickly become aware of your new cat's presence. The cats will usually sniff at each other under the closed door. Do not be surprised if there is some initial hissing. Help the cats get used to each other's scent by rubbing a towel over each of them in turn. Feeding them on either side of the door that closes off the room the new cat is in is also helpful. They will start associating the smell of the other cat with a good thing (food). After a few days, take the new cat out of its room, put the old cat in that room with the door closed, and let the new cat begin to explore the rest of the house for a few hours each evening.
The next step is to let the cats see each other, yet still keep them separated. An old screen door or a piece of Plexiglas works well for this. Another option is to prop open the door of the new cat's room, just enough so that the cats can see each other and put a paw through, but not enough that they can get through the door. After a few days of this, try feeding the cats together, but at opposite ends of the room. Monitor the cats during this time, and separate them except at mealtime. Each day, move the food dishes very slightly closer to each other, until the cats are eating side by side. The idea is for the cats to associate each other with the pleasant experience of eating. It is not unusual to hear occasional hissing, but this should decrease as the days go by. If things do not seem to be improving, try decreasing their interaction for a few days.
Once the cats seem comfortable with each other, you can move on to the final step. Open the door all the way, allowing the cats to come and go as they please. Monitor them closely, in case they fight. Do not leave them alone for any length of time until you are sure they will get along well. Make sure there is at least one litter box per cat. This helps to prevent a more dominant cat from stalking the other and keeping him from using the litter box.