I deal with this on a very regular basis.
Personally, I dip all my corals. I use Interceptor (yes, the kind for dogs), Fluke tabs (the kind you get at your pet store for fish medicine), and occasionally Iodine (the aforementioned Lugol's solution), and occasionally Potassium Permanganate (if its a Montipora sp.).
I usually remount the branching type corals onto acrylic rods and insert the rods into holes I drilled in all of my rocks with a 1/2 Bosch masonry bit. This method is called "pegging".
Sometimes, if its an encrusting type, I will cut away the base of the plug, make it more of a disk, and glue that to a larger flat stone to get a bigger piece to work with later, to experiment with positioning (to determine the coral's lighting and flow preferences, plus start it low if unsure) before committing to a particular larger rock to glue it to. But you can do the same and just glue that disk to your rockwork if you have a permanent spot where you know you will want it forever, and want it to start encrusting everywhere from. You can do this with superglue and/or 2 part epoxy. With superglue (the kind for corals, a gel-type such as IC-Gel or any of the commercial kinds marketed as for fragging) you squeeze out a half-marble size onto the bottom of the plug, dip that into the tank water to make it skin over, and then roll up your sleeve and put it right down into the tank and slam it down on the spot where you want it to stay. Mold the glue with your fingers and believe it or not you can shape it and work with it a bit before it sets. If you want to build a ramp for the encrusting to occur easier and basically make a ramp to train the coral to grow better outwards vs. down into some shadow, you can use 2-part epoxy, mix up a small shooter-marble size into a ball, then make it into a snake with your palms, then put that into the tank and go around the base of the disk you glued down and mold that as an intermediate "step" for the coral to grow onto on its way down to the rock. This is good to do because the corals may come to more of a halt when growing when they grow into a shadow (where the side of the disk goes straight down). So this can speed things up for you and the final look is certainly more natural as well.
As stated above, to reiterate, if unsure, start low and bring the coral up towards the light. It's easier to give it more light than to make it recover from being burned. Also, your lights will matter as to decide where to position on day 1 in your tank, also try to determine the light of the tank it came from. To go from 20K lights at the bottom of a tank to 10K lights at the top would easily fry your delicate frag.
Hope the info helps and if you have any questions, ask away, more than happy to help.