DO NOT LET THE NEWCOMER AND THE RESIDENT CAT MEET AT FIRST. The newcomer will be nervous upon arrival not knowing where he or she is. The newcomer will emit an odor of fear (that we cannot smell but the existing cat will.) After a day or two, that smell will disappear and a meeting of the two cats will go much better.
Restrict the newcomer to one room. In that room, place rood and water dishes, a bed(a blanket or towel will do), various toys and a litter box as far away as possible from the food dish(you wouldn't like it if you ate next to your toilet would you?) Visit and play with the newcomer as often as you can. But, make sure that you pay special attention to your resident cat as well.
Allow newcomer and resident cat to be separated for at least one to two weeks.
Meanwhile, rotate blankets and toys between cats so your resident cat smells the newcomer's things and the newcomer gets a whiff of the resident cat's things.
After about ten days, allow the newcomer to roam the house and the resident cat to tour the newcomer's room for an hour ot two at a time. Do this once a day for the next ten days, if you can. The cats will mark each other's territories with their own scents using their cheek pads.
When it is time to introduce the cats, do so gradually beginning with a mere few minutes of togetherness at a time. During these brief meetings, give each cat a tempting treat such as chicken, baby good, plain low fat yogurt or tuna. Each will quickly learn that it receives a treat only when the other cat is present. If all goes well, begin to let the cats interact. There may be some hissing and the resident cat will assert itself, but that is to be expected. It may also be helpful to have an interactive toy such as a clothesline or round ball track toy that will interest each cat but keep them separate during play. You can wiggle BOTH ends of the clothesline with a cat at either end and before you know it they will both be playing together without realizing it.
It is best to separate them at dinnertime. If you allow free feeding, and the newcomer is a kitten, put a hole in a carton or box just big enough for the kitten to squeeze into, but not large enough for the adult cat. Put the kitten's food dish inside the box, where the kitten will eat, and the older cat's food dish outside the box. Separate litter pans may be necessary until it is apparant that the resident cat does not mind sharing. Following these suggestions may ensure a long and happy relationship between your two new friends!