Have cats already at home?
Help your new feline friend's Settling-in process with proper intro protocols:
Steps to take:
Set up a comfortable "safe room" or Basecamp for the New Cat. Put food, water, litter box (not near the food), scratching post, toys, and bed or other sleeping mat there.
Expect some "hissy-spitty" behavior through the closed door from both cats. This is natural and normal; they are just starting to explore their "pecking order."
Scent is very important for cats. Let each of them smell the other indirectly, by rubbing a towel on one and letting the other smell it. They will soon accept the other cat's scent as a normal part of the house.
Once or twice, switch roles. Put New Cat in the normal living quarters, and let your resident cat sniff out the new cat's Basecamp.
After a day or so, let the two cats sniff each other through a baby-gate or through a barely-opened door. Gauge the rate at which they seem to be acclimating to each other.
When you think they're ready, let them mingle under your supervision. Ignore hissing and growling, but you may have to intervene if a physical battle breaks out. Again, take this step slowly, depending on how quickly they get along. If they do seem to tolerate each other, even begrudgingly, praise both of them profusely.
Make their first activities together enjoyable ones so they will learn to associate pleasure with the presence of the other cat. Feeding (with their own separate dishes), playing, and petting. Keep up with the praise.
If things start going badly, separate them again, and then start where you left off. If one cat seems to consistently be the aggressor, give them some "time out," then try again a little bit later.
The introduction can take from two hours to six months, so don't be discouraged if your cats don't seem to get along well at first. Often the case is that they will eventually be best buddies.
Factors to Consider:
If you already have more than one cat, use the "alpha cat" for preliminary introductions. Once he/she accepts the newcomer, the other resident cats will quickly fall in line.
Lots of snuggle-time and attention is indicated for all cats concerned during this period.
The more Catification you have in your home, the easier this process will be.
With patience and perseverance, you can turn what might appear at first as an armed camp into a haven of peace for your integrated feline family. Congratulations on giving another cat in need a permanent home!
Jackson Galaxy has a series of Cat Intro Videos you should check out for more info: