For fragging corals like xenia, leather, colt, kenya tree cut off the frag with a razor blade. Then use a needle and fishing line to tie the frag to a rock or frag plug. Poke the needle through the coral in a couple of places to sew the frag to the rock. In a couple of weeks you can cut the line away, as the coral will have attached to the rock.

For SPS frags, make a sharp break and immediately dip the coral in an iodine or coral cure solution, I prefer ReVive. Then super glue the coral to the plug using super glue gel.