Softies-generally the easiest to frag. You can cut them off with scissors or a razor blade, but the issue then is reattaching them. Most softies have a mucus that prevents them from being directly glued on things. You would have to let the softie attach to something on its own. Reefers usually will put it in some sort of container in the aquarium (like a little tupperware), the bottom of the container they will fill with rubble, and put the frags on top of the rubble to attach. This would be the more difficult way to frag the softies. Easier would be to use a bone cutter and chip under the rock of the softies you want to frag. This way the zoas or polyps or whatever will still be attached to some rock, and you can just go ahead and glue the frags to where you want.
SPS- just involves using bone cutters or your hands (depending on how concerned you are with the sensitivity of the coral/cleanness of the cut) to cut off branches assuming its a branching coral. You can't really frag encrusting sps very easily, unless they are growing on a thin rock that you can cut with bone cutters. Often, you cannot cut off sections of encrusting sps because they are often growing on thicker rocks that you can't really cut with your bone cutters. The next best thing is to put pieces of rubble around the encrusting sps and let it grow onto the rubble which you can break off when you want.
LPS- these are generally the hardest to frag. I'm not very familiar with how its done, and have never done it, but from what I have read usually some sort of mechanical saw is used to cut through the LPS skeleton.