there is a book by anthony calfo which i have been unable to track down here in portland so far (might have to mail order it) which has been described to me as the bible of fragging. it is called aquarium coral propigation and gardening or some such. you can do a search for anthony calfo and will get a couple hits with reviews and pop ups to buy it. the techniques vary drastically depending on what type of coral you are working with, but the general method is to break off or cut off a piece of the main colony, then it is attatched to a new piece of rock or rubble, and it is then given time to grow out and permanently attatch its self to the new home. attatchment can be done with superglue, a needle and thread, toothpicks, fishing line, netting.... all kinds of stuff, and cuttings can be taken with a dremel, shears, scalpel, xacto knife, etc.
for more specific details you can search for fragging techniques for a specific species, or reference a book like the one listed above. i frag a lot of soft corals and have inadvertently fragged a few hard corals... as long as your water conditions and setup are conducive to coral growth, almost all coral colonies can be fragged in one way or another.