Clean the surface of the broken area completely with a sponge and a mild cleaning agent, such as dish soap. Rinse the surface well with clean water. Let it dry for at least 24 hours before you apply the patch material so any water that might have gotten into the stone cracks has a chance to dry out.
Apply the patch material according to the manufacturer's directions, as different manufactures have different mixing and application methods. As a rule, the most common way is to smear the compound over the cracked or broken area with the application tool (which resembles a putty knife). Let it dry according to the manufacturer's directions and clean off the excess from the face.
Spray a coat of sealer across the marble surface and let it soak in according to the product's label. Wipe any excess off with an old towel and check the surface to see if it has been sealed properly. Apply a droplet of water to the surface of your marble and check to see if it puddles up. If it soaks in, you need another coat.