How can I introduce a new cat (a stray that I found) to my household of one very, very spoiled cat, who has "ruled the roost" alone for the past four years?
First, be sure that your new kitty is tested for Feline Leukemia Virus (FeLV) and the Feline Immunodeficiency Virus (FIV). If she is negative for both of these diseases, then she should be pretty safe around your cat. Still, quarantine her for one week (two to three weeks is even better); then put her in her own room in your house to start the introduction process.
The key to introducing a new pet is to GO SLOW! Give the new cat about one to two weeks in her own room where the two cats can sniff each other under the door. Once they are doing this with minimal hissing, switch the situation. Put your cat in the room for a few hours and let the new kitty roam the house. This allows the resident cat to smell the new cat’s scent and explore without worrying about having to fight the newcomer. It also allows the new cat to explore the new house and become familiar with hiding areas.
The next step is to let them see each other from across a room or through a tall baby gate you put across the doorway of the room where the new kitty is. Then, when they’re used to this, let the cats out together SUPERVISED, and put down a treat (canned cat food, tuna, etc.). Use two dishes on opposite sides of the room so that both cats are in the same room eating their special treat. Do this at roughly the same time every day, and soon the cats will be running to be in the same place at the same time. When hissing and growling subsides, then start moving the dishes closer together. If they start growling at each other, you have moved the dishes too close, too quickly and need to back off. Soon they will associate a good thing with seeing each other.
Do not let them together unsupervised, as they could fight and hurt each other. The entire process will probably take about 6 weeks, and even then they may not be buddies but can be in the same room without hissing at each other. Good luck, and remember -- patience!
Information taken from HealthyPet.com