In a nutshell: take it slow.
Bringing a new cat into the household can be a traumatic experience for all involved. I know cats who continue to hiss at each other even years after becoming roommates. Other cats seem to get along within a few days. How can you tell which scenario will happen, and how can you make it easier for both cats?
How Will Your Cat Feel About Another Cat?
Some cats will never accept a newcomer. If you have a cat who becomes tense and alert when she hears another cat on television, or who has been known to hiss and growl at a cat she sees out the window, these are signs you have an "only child" on your hands. However, if your cat is casual and unconcerned when she sees other cats, this is an encouraging sign.
Past behavior is a good indicator of future performance. Has your cat ever lived with other cats before? How did it go? Did she hide, fight, ignore, or actually cuddle the other felines?
Age makes a difference, too. All cats grow up with other siblings in their litter. The younger the cat, the easier it will adapt to these new circumstances.
How Can You Make The Transition Easier?
In a nutshell: take it slow. Set up a separate area for the new cat, whether it's a spare room, the bathroom, or a large dog crate. (If you have any friends, family members, or coworkers with dogs, ask around for a crate you can borrow.) Give it several days for the cats to get used to the existence of another cat before you take the next step.
Have patience. Be prepared to spend up to a month in the transition between "cat in separate room" to "two cats in the same space." Figure out all the steps in between, and pace them out accordingly. The specific steps will depend on your arrangement.
At each transition, expect some hissing and growling. Have a squirt bottle handy, or be ready to clap your hands loudly if they begin to fight. Do not attempt to break up the fight by hand!
You will know it's time for your cat to "level up" and go to the next stage when both cats relax and become bored with the current stage. Grooming, eating, and yawning are all signs that a cat is relaxed. Your biggest goal is to avoid a situation where either cat will be surprised and startled. Remain calm, spend a lot of time reassuring both cats, and know that your patience will be well rewarded in the long run!