Remember to take things slowly! You don't want to stress out your resident cat any more than necessary to introduce the new addition. First, remember that cats are territorial, and this is a survival instinct. In the wild, a new cat moving into the resident cat's territory means less food for the resident cat! This leads to fights and marking behavior in the wild, and can cause similar problems in the home (urinating and defecating outside the litter box, etc.)
1.Start your new cat out in one room. Let him get used to the new room, keep his litter box in there and feed him there. Give him a few days of your family's attention, without the other cat around. It's ok to let the cats sniff each other under the door. There may be growling and hissing.
2.After a few days, introduce the new cat to a wider area of the home. Still keep them separated. You can put the resident cat in another room for short periods while the new cat is out exploring. This way when they are eventually together, the newer cat will have found some spots to get away from the older cat, if the older cat gets aggressive.
3.After a few more days, switch the cats. Put the older cat in the new cat's room, and vice versa. Let them sniff and smell each other's presence in the rooms. During all this time, the older cat should be getting lots and lots of attention. Make sure she knows she will still get loved, played with and fed, regardless of any new additions.
4.By now hopefully they are ready for a brief introduction. Sometimes I have tried putting one of the cats in a carrier, and letting the other sniff it. Then after a while switching them. If there has been lots of hissing and growling, definitely start with carriers. You can give both cats treats to reinforce the idea that being together is a good thing. If there is minimal hissing and swatting, allow the cats together in the same room and bring out a toy on a string, or a laser mouse, and play with them both. Older cats tend to back off a bit and let the younger ones go for it. Again, treats are good encouragement.
5.Even if everything seems to be going well, don't leave the cats together in the same room when you are gone or asleep yet. Give them time to get adjusted to each other's presence. When the new cat is a kitten, all this will likely happen faster than if the new cat is an adult.
6.Above all, make sure the resident cat doesn't feel neglected. Give him tons of attention, even though you might be inclined to want to play with that cute new kitten. Let the kitten and the resident cat bond with each other, and don't worry about you bonding with the kitten. You have plenty of time for that, it happens at any age. Also make sure the new cat doesn't steal the resident cat's food, as this will cause a lot of conflict. If necessary, feed them in separate rooms. Kittens especially don't understand the "your bowl, my bowl" concept. If it's food it must be theirs!!!!