Purchase a Dremel tool with a variety of cutting, polishing, and sanding heads and mounts for them. Purchase some magnifying safety glasses, a safety mask, and safety gloves.
Choose the coral that you'll be cutting carefully. The larger it is, the better your results will be at first.
Set up the Dremel tool and equipment on a solid table in a work area that has plenty of ventilation. Place the coral nearby. Arrange the safety magnifying glasses, gloves, and air filter mask for use.
Put a medium- to small-sized cutting wheel on the Dremel and tighten it down. Coral is not hard to cut in terms of the Moh's Scale of Hardness. It has a hardness of about 3.5 out of 10. Plug the Dremel tool in once the cutting wheel is mounted and secured tightly.
Draw a faint outline on the coral to mark the areas you'll be cutting off the stone and trimming down. Use a pencil or ink pen for this. It helps to have guidelines drawn right on the stone itself so you can follow them when using the Dremel tool to make the cuts.
Put on the air filter mask and adjust it to fit your face and nose. Put on the safety magnifying glasses and safety gloves.
Grip the coral firmly between your fingers on one hand, with the side you'll start cutting facing outward.
Hold on to the Dremel rotary tool firmly in the other hand, keeping your thumb near the on/off switch. Turn the Dremel on. Get a feel for how fast the cutting blade is spinning so you know what kind of force will be applied to the stone when you cut it. Keep your fingers out of the way.
Cut away at the coral with the Dremel tool. Manipulate the coral around with your fingers as you use the tool to cut off the areas you drew on the stone. When finished cutting, consider polishing the coral with a polishing wheel mounted on the Dremel.