Desensitization through Gradual Exposure and Positive Association
There are many techniques for introducing cats. They are all based on the same principle:

the cats to each other's presence so they no longer feel threatened.
This is achieved by -

1. Making the exposure gradual.

Gradual exposure decreases the cat's "fight or flight" responses in the presence of an intruder, to the point that it is no longer triggered and he or she can learn to accept the presence of another cat in their territory.

2. Creating positive associations.

Many techniques rely on distracting the cat with positive stimuli while in the presence of the other cat. This creates a positive association with the other cat, reducing aggression levels.

While on the subject of positive associations: Make sure you don't end up creating any negative associations during the introduction process. No matter what the cats do, or how the process goes, keep your tone of voice calm and avoid scaring the cats in any way.

Introduction Techniques
The following techniques utilize at least one of the principles detailed above and sometimes both.

1. Scent Desensitization
Scent is central to your cat's perception of the world. Take a clean sock and put it on your hand, then pet the new cat with your sock-clad hand. Focus on rubbing the cat's face, chin and cheeks. You are in fact lacing the sock with the scent of that cat. Next, leave the newcomer's room and return to your resident cat's "territory". Place the sock within the cat's reach. Don't call the cat over or initiate any interaction with the sock. Allow the resident cat time to find the sock and investigate the new smell. He or she may react with fear or aggression. Just let the cat be and make sure the environment around them is calm (yourself included!)

Do the same thing with the opposite setup. Use a clean sock (not the same one!) to soak up scent from the resident cat, and place that sock in the newcomer's room. Repeat this once a day for several days, until you see a reduction in both cats' reactions to the socks. If your cat is a fan of treats, you could try and offer one as she's sniffing the sock to create a positive association with the scent.

2. Visual Desensitization
Once both cats are desensitized to scents, you can move on to the next sense: vision. The challenge here is to allow the cats to view each other, without letting them engage in direct physical contact. Cat behaviorist Pam Johnson-Bennett suggests using three baby gates, one on top of the other, to create a gate the size of your door which you can use as an additional door to the new cat's room. A screen door works too. Behaviorist Jackson Galaxy suggests sticking with the regular door and just opening it up a crack, allowing the cats to view each other in a controlled way.

Allow the two cats to see each other. Don't be alarmed if they show aggression, and stay calm. You can use treats to make the session more pleasant. Jackson Galaxy even suggests feeding the cats when in this situation. According to his method, you should limit feeding to the times when the cats see each other through the crack in the door, placing their food dishes far away at first, and bringing the dishes closer every day.

3. Interactive Playtime & Treats
You can vary introduction techniques a little bit, and change them based on what you know about your own cats. Some cats couldn't care less about food or treats when they see another cat and may prefer playtime instead. Remember the principles behind the techniques and you should be ok. If need be, create the positive association by interactive playtime with your cat. Read more on how to conduct playtime sessions with your cat.

Keep in mind that some cats may be extremely tense in the presence of a cat they don't know or trust. Whether playing or providing treats, stay in control of the interaction and don't allow them to come into physical contact too soon. Watch out for re-directed aggression as well. A cat may become all worked up over the other cat's presence and lash out at you with no warning. When playing during introduction sessions, keep your hands out of reach and use only fishing-rod toys.

How Long Should This Take?
It really is hard to predict. A lot depends on both cats' temperaments. Generally speaking, it's much easier to introduce kittens to each other than adult cats. Some adult cats are very cat-friendly and will gladly accept the company of a new cat. Others may always prefer to be the only cat in the house and never fully accept another cat's presence.

As you move forward with introductions, watch the cats' body language and try to assess their cues. Don't move forward before both cats are calm. It's better to take a few more days before moving on to the next stage than risk a cat fight.