Razor blade for green star, softies, etc. Once also fragged a cabbage leather without having it pitch a chemical fiit by putting a rubber band around the creature, down the line I wanted separation. His tissue grew thinner under the pressure, and I was able to separate the halves with less damage and no chemical damage to my tank. (They spit, furiously, if annoyed. Or because they just want to.)
Stony branching coral is generally easy. Most times you can break a head off by hand. If it's montipora (sps) it'll break at a touch, and glass-cleaning usually results in some montipora broken. But the shed pieces will also grow if they have light. There are a few stonies that are much tougher, and require some of the fancy cutting tools you may find for sale.
Beginners should avoid fragging 'wall' corals, meaning corals that form one mass that can't be broken by hand. Fox, bubble, some hammer (a species which usually grows in heads) etc,
Encrusting corals should be done as billdogg says: set rubble near them and sell what creeps over onto other rocks.
If you are fragging a mushroom, be sure to make a cut that includes part of the mouth.
If you are fragging a palythoa (similar to a zooanthid, but usually larger and has long eyelashes) glove up, mask up, put on goggles, and scrub up when finished, disposing of the water you used very carefully, and running carbon in your tank (a good idea with any newly-fragged coral that you are keeping. Palythoas can mean hospital-time if you get it on eyes, mouth, or broken skin. They are quite toxic. Be sure when you buy any button coral which camp it belongs to. Zooanthids are tame; palythoas are serious toxin.
