A cat's usual reaction to unwelcome changes in its living situation is to distance itself from the newcomer. Your existing cat will usually exhibit one of two kinds of behavior with the newcomer — he will hide out, even if it is for a few days refusing to acknowledge the newcomer's presence, or he may act aggressively towards the newcomer in an attempt to persuade it to retreat. It would be advisable not to try and force a relationship on either cat at the onset of an introduction.
You should allow the cats to adapt at their own speed and keep in mind that cats are extremely territorial and become strongly attached to their familiar living area. Some cats will take days to adapt and others may take weeks, and in some cases months. The newcomer needs to be given an area where he can retreat if he becomes threatened or frightened, leaving him in a spare room with the door closed for the first few days so the resident cat can adjust to the scent of the newcomer is usually a good idea. This way they can smell each other but they cannot hurt each other.
Make sure your newcomer has a litter box in his area along with food and water. By providing the newcomer with a place of his own, you are giving him familiar territory and allowing him to have security so he can rebuild his confidence to venture forth once you leave the door to his room ajar.
When selecting a new cat, try and find one that has lived with other cats. A cat that is similar in age and sex to the resident cat will be accepted more readily. A kitten is ideal. The likelihood of fighting may be reduced and usually eliminated by castrating all the toms or spaying all the females. The owner should not intervene — by taking sides, showing preferences or breaking up fights you will only make matters worse. Just give them plenty of time — the longer the cats are left together the more they will tolerate each other's presence and maybe even begin to enjoy each other's company. If the owner feels that things are just not working out and decides to get rid of the newcomer, he/she should not think of introducing another, as this will further stress the resident cats. It is seldom the newcomer that is at fault. Usually the existing social scene does not readily welcome another member.