The first step in the introduction is to take the towel that your new cat has been sleeping on and put it where the other cat usually sleeps. At the same time, take something that has your first cat’s scent on it, like a pillow or a toy she plays with a lot, and put it in the new cat’s room. Cats identify each other by smell, and this step allows them to get used to each other without actually having to come face to face. Next, try opening the door a little so the cats can get a peek at each other. If you happen to have a childproof gate, you can open the door and gate the room so that they can interact safely. Don’t force them together though! Cats refuse to be forced to do anything, and that can only make them more wary of each other.
The next step is to allow your new kitty to explore your entire home. If you just let her out of the room, chances are she will be more concerned with her new roommate than with discovering where everything is. So put the other cat in her carrier and let the new guy poke around. Once she has had a chance to see everything, you have arrived at the moment of truth. Open the carrier and let the two cats meet face to face. There may be some hissing or swatting, and one of them might make a mad dash under the bed. The unfortunate truth is that there is a distinct hierarchy in feline society. Unless your cats are both kittens, chances are good that there will be some posturing and mean behavior while they figure out who the boss is. You may feel bad for the cat that comes out on the bottom, but there is little you can do to change it. At this point you have to let them figure it out for themselves. Just make sure no one is getting physically injured. If that is the case, put the new cat back in its room and try again later. If after several attempts at introducing your cats, they are still fighting to the extent that one is getting injured, you should consider consulting a veterinarian, and as a last resort, finding another home for your new cat.