What queensheba said is almost exactly what I do. I add one "house visit" where the preexisting cats are corralled in a different room and the new cat gets to explore the digs by himself.

If there's much growling or hissing when they first see each other through the open door, I also add a baby gate phase where they can see, hear, and smell each other but can't effectively fight. (This phase is deeply annoying for the human as I need four baby gates to seal off a doorway and it's hard for ME to get through!) I've freecycled a lot of baby gates. :-)