Imagine that all of a sudden someone decides that you are going to have a roommate, a new person living in your home, without asking you. You have to share space, even the bathroom. This can be a difficult transition for humans and the same for cats.
When introducing a new cat to your pet cat, there are a number of steps to follow carefully.
SMELL AND HEAR INTRODUCTION
To play it safe, the two cats should be able to smell and hear -- not see or touch-- each other. This will prevent that awkward first direct encounter. Place them in adjoining rooms with the door closed. Each cat should have their own water and food bowl, bed, scratching post and litter. Be sure to buy new ones for new cat so his new home environment is not overwhelmed with the scent of the other cat. You will gradually introduce their scent to each other. Feed the cats near the door that separates them so they gradually learn that coming together (even though they can't see eachother) results in a positive experience.
After four days, switch their locations so they can familiarize themselves with the other's smell. This also allows the new cat to explore a new section of the home.
RUBBING WITH TOWELS INTRODUCTION
Some behaviorists suggest rubbing the cats separately with the same towel to intermix their scents. First gently rub one cat with the towel. Then rub the other cat. After the towel carries both cats’ scents, bring the towel back to the first cat and rub her with it again. If the reaction is positive, then reward the cats with treats. This is important. Just like training a dog, you need to find a treat that they love. Something extra special.
After a few more days, play with each of the cats near the door. Encourage them to paw at toys under the door. Eventually the cats may play “paws” under the door with each other.
LOOK BUT DON'T TOUCH INTRODUCTION
After 10 days, you can introduce the cats to eachother assuming there are no regular signs of hissing or aggression during their separation. This is the "look but don't touch" phase. Instead of a solid wood door, try to use a glass door or even better a screen door or two baby gates, (one on top of the other). Here the help of a friend is a good idea. Each person places the cat a few feet away from the separation gate. When the cats notice eachother, say their name and toss treats behind them, away from the gate.
Over the next several days, continue feeding, playing and feeding treats near the gate and gradually getting closer to the gate.
FACE TO FACE
If all goes well above, then it's time to meet face to face. These introductions must be carefully supervised. Bring them together when they are calm, let's say after a meal or exhausting playtime. Some experts recommend a water bottle to use if one starts to misbehave. As the cats become more familiar with each other, allow them longer and longer periods of time together.
If you have multiple pet cats, introduce the new cat one by one.
Also cats are either bush dwellers or tree climbers. Make sure you know your cat and have sufficient cat or people furniture they are permitted to use for their own exercise and enjoyment. Otherwise pent up aggression occurs and is exhibited in disruptive behavior. Remember with negative behavior, such as peeing outside the litter box, the cat is communicating that something is wrong. It's either medical (please see a vet) or there is something uncomfortable in the cat's environment. Keep mental note of changes such as not cleaning the litter enough, did you move litter box or cat's favorite furniture? etc.
Some cats will get along and play together and become bosom buddies. Others may not. It's important they at least respect one another. The key is consistency. Cats are trainable but consistency in the very beginning is critical. If for some reason you followed the steps and are having difficulty, there are expert cat trainers that can help you with more complex cat behaviors.
BASIC NEEDS/CREATURE COMFORTS, they don't need much
Ensuring there is proper cat space, furniture, litter boxes (one per cat plus one extra), scratching posts, accessible water is important to ensuring a happy home environment for the cats and you. No one likes a sour puss.