Cats are highly territorial and lack the high degree of social skills that we human beings possess. Hence, introducing a new cat to another needs a lot of planning and a patient approach. It may take around 12 days for kittens and young cats, and 12 weeks or more for older cats to get comfortable with other cats.
Points to Consider
There are certain things that should be kept in mind while introducing a new cat to an old cat. In an ideal situation, the new cat should be younger than the existing cat in the household. In case you don't want litter in your house, don't get a new cat of the opposite gender. In case you can't avoid this, consider neutering either of them.
In any case, it is always advisable to spray female cats in order to spare them the discomfort of the heat cycle. Check if the new cat has any disease. While introducing a new cat, one needs to ensure that the new feline is not carrying parasites or pests or diseases that may easily transfer to the others.
Firstly, this would cause least amount of inconvenience to the existing cat. This is a very important aspect of introducing a new cat to your cat, as, if the existing cat feels that he is being given less attention and care due to the new one, he will develop an antagonistic attitude towards the newcomer, and this he might nurture his entire life.
Secondly, it will give the new feline time to settle down in this new environment. This would be good for the new cat's health too, as it has been found that cats suffer more from environmental stress than from social challenges.
Allow your older cat to sniff and explore the carrier, and observe how it reacts to the scent of the new member in the household. Spend time with your older cat like you always do. Play with it and pet it. In between, go into the isolation zone and feed and talk to your new bundle of joy.
Don't rush in case it makes a mad rush at you. It might feel excited and comfortable already. However, you really don't want to scare it, do you? Then wash your hands and go back to your older cat and play with it.
You may also note it expressing displeasure at the change in 'its' home. However, let your cat take its time. Unless the aggressive behavior has subsided or till it has become comfortable with the new scent, do not change anything around.
Just Eye Contact Please
Once the first level of comfort has been achieved, it's time to move a step further. Install rigid plastic mesh baby gates or high-tension gates, high enough to prevent the two cats climbing over it.
Alternately, you could also fix rubber stoppers on either side of the door, so that the door can't be pushed on either side once you have kept the door ajar and fixed the stoppers on either side. Don't leave the door open more than about 2 to 3 inches. Ensure that the cats are only able to see each other, but do not come in contact.
A Little Closer Now
Once the cats have got used to the smell and sight of each other, then comes the time to see how comfortable they would be in the physical presence of each other. Remove the gates that had been installed on the doorway of the isolation room. Do this while the existing cat is engaged somewhere else.
Let this occasion pass by just as unceremoniously as possible. Let the cats get to know each other on their own. Expect some amount of chasing and stalking. This is the territorial instinct which is an integral part of cat behavior. Even if they fight, try to stay out of it as much as possible.
Cat fights sound worse than they really are. Clapping, shouting or throwing water usually ends the fight. However, if you have to intervene, do not handle them directly. Put a thick blanket over the felines and then lift up one of them, and put it behind closed doors. Check for wounds after each has calmed down.
In case tension brews up considerably during the next attempt of introduction, try feeding them side by side with the new cat in a cattery cage that is set up in the older cat's area.
The main point that needs to be remembered is that the beginning needs to be right. While the older cat should not feel that it is being neglected or its space is being encroached upon, the new cat must get enough time to settle in the altered environment, and feel secure with new people and cats around.