Keep Them Separated
When you bring your new cat home, have a special place set up for them. A guest room or the bathroom is ideal. Put food, water and litter box in the room along with toys and a scratching post. Keep your new cat in this room, away from your other cat(s) for about a week. It is tempting to let them interact right away, but you will have much better luck if you wait.
Introduce the Smell First
To a cat, a sniff is worth a thousand words. To get your existing cat use to the smell of your new cat, rub a towel or washcloth gently over the new cat. Let your cat(s) smell the towel, but don't be surprised if your cats start to hiss. Hissing and growling are normal reactions so don't scold them when they hiss or growl. Do the same with your existing cat so the new cat can smell them too.
Encourage Interaction through the Door
Place your new cat's food near the door of the room so he/she will stay near the door. Your cat will smell and hear the new cat through the door. Give your cat treats and/or catnip near the door of the new cats room so that he associates it with good things.
Let Them Roam Alone
Lock up your cat in the bedroom, and let the new cat roam around the house. This lets them explore and exercise, and it also helps them find good hiding places for later. Then put your new cat back in its room and let your old cat walk around and smell them without having to see the new cat. This is another good way to get them use to each other's scent.
Open the Door a Crack
After a few days, carefully open the door a crack so the cats can see each other but can't stick their heads out. Be prepared for some hissing and growling, but if one tries to smack the other, close the door. Do often a few times a day.
Let Them Out
Bringing a new cat into the house is not unlike introducing a baby to an older sibling. Jealousy and pouting are normal reactions. Even though you are excited about the new member of your family, do not forget the cat that has been your faithful companion until now. Do not yell, scold or punish them for hissing at the newcomer. They may not react like they way you want them to right away, but your cats will come around.
When the time comes to let the new cat out to mix with your family and other pets (do not rush - wait a week) and be sure to monitor closely, open the door to see what happens. Most likely your existing cat will hiss and growl, maybe even wail, confirming their worst fears. Unless open fighting breaks out, let them hiss as cats need to establish hierarchy and territorial rights. Even though the growling is upsetting and sounds bad, it's okay. Reassure your cat verbally and pet him if you can (he may not let you because he's upset so don't take it personally). When the cat is nice or at least non-threatening to the
new cat, praise your cat lavishly and give them treats.
Do Not Expect True Love
We all wish our cats would become best buddies and curl up together, lick each other, etc., but unfortunately this does not always happen. However, your cat and the new cat will at least form a truce. They may not want to hang out together, but they will eventually respect each other's space and stop hissing.
Don't worry if your cats never become best friends because they will still keep each other company and they will both love you.