I'm very lucky Dawn, all my residents cats are very laid back and used to seeing new arrivals so it doesn't really phase them.
I think cats can sense when humans are tense and will "play" on it so the calmer you are in these situations, the calmer the cats will be.
Also, always make sure you give plenty of fuss to the current occupants as well as the new resident.
I am definitely no expert and I know some people have alot of trouble with introductions so I guess I have just been very lucky. The only real bad one I have had was Hershe recently. Stella definitely took a dislike to her, but I moved Hershe to live with the downstairs cats (we live in a three storey townhouse, the cats downstairs can go out during the day), and she settled in fine down there, although she will not go out, just sits in the window. I would not say they are all great friends but they all find their little spaces and co-habit amicably and some do form very special friendships.