Bringing home a new cat or kitten can be a very exciting experience for you, but a traumatic one for your resident cat(s) and the new arrival.  A proper introduction will go a long way to help smooth the stress caused by the new arrival.

It is important to keep the new cat isolated for a period of time.  Make sure the isolated cat has access to food, water, and a litter box (since cats don't like to eat in the same place they eliminate, make sure the box is as far from the food and water as possible).  During this time, feed the cats on opposite sides of the door separating them.  This will help them to get used to each other and foster good feelings while they are in one another's presence.

When the cats seem comfortable being around the door (no more hissing or growling), move on to the next stage.  Open the door just a bit and prop or latch it so the cats can't push it open any further.  Now they can see each other, so expect some hissing at first.  Continue to feed on opposite sides of the door and don't scold them for hissing.  That's a natural reaction and as long as it doesn't escalate into fighting, it's acceptable.

After the cats are fine being able to see each other, the next step is to let them have guarded access to one another.  You can put the resident cat in a cat carrier or separate room and let the new cat explore.  During the whole process, it will help to rotate the rooms that the cats are in.  For several hours each day, put the resident cat in the new cat's room, and let the new cat roam around the rest of the house.  This helps to prevent territoriality; it lets the resident cat check out the smell of the new cat and lets the new cat explore the rest of where s/he will be living.

There is no set schedule for all this.  Some cats are fine with a new cat after a day or two, some cats take a month or more.  The important thing to keep in mind is that the first few weeks of the cats' relationship will set the stage for the rest of their lives together.  The most common mistakes people make are: trying to rush things and not having enough litter boxes (see Litter Boxes).  Be patient.  There are very few cats that will not eventually get to the point of being able to coexist happily.

One other very important thing to keep in mind is to make sure that your resident cat gets lots and lots of attention during this time.  From her perspective, there is an intruder in her territory, one that she didn't get to offer her opinion about.  Though it may be very difficult not to spend all your time with the new cat, remember that this is a pretty big stress on the resident cat and give her some extra time and attention.