I'm also interested in this. I've had no problems with my coral so far, so the way I do it seems to work. However I'm curious to hear other approaches.
When I get my coral i pour it and the water it came in, into a small container. Then I add small amounts ,5-10 ml, of my tanks water to the container. Only adding every minute or two. Then once the water in the container has doubled, I take the coral and add it to my tank.
I have some pretty hardy coral so maybe that won't work for some coral but it's worked so far.
My corals include: mushrooms, zoas, torches, and a birdnest.
I have noticed that the first week or so you really have to be careful with the light. When I first introduced my torches, they had a good response to my light. They opened up twice the size of what they were at my lFS
within an hour of introduction. My birdnest on the other hand did not fair so well. I introduced it and noticed that it progressively got whiter and whiter. It was too close to my light and started bleaching. So I redirected the light in my tank and am slowl moving it back towards the birdnest. My birdsnest is super fuzzy now and the white parts are filling in too! Here are some pictures of my corals