Some will actually use the plug and glue it to the rock with an Epoxy. Personally, I don't like the look of seeing white plugs everywhere in the tank, even though they'll eventually get covered up by the base of the coral.
I'll usually use a metal scraper, razor blade, etc. and try to get as much of the coral off in one piece as I can. If you end up with a little still on the plug, you can either leave it and let it grow into a new frag, or just toss it.
As for gluing the actual frag to your rock, use superglue. Superglue doesn't seem to actually stick underwater, but if you apply it in the air (even if its still wet), hold the frag in place and dunk it underwater. By doing so, it will make the outside of the glue dry and help hold it in place. I usually will set it on the sandbed in a low flow area until the glue is done curing. Also, some people glue frags to the big pieces of rock, I don't. I'll grab a piece of rubble, superglue the frag to it, then epoxy/superglue the rubble to one of the big rocks.