Clean the entire area around the crack with a clean towel or sponge and ensure that it is completely dry before you attempt to fill the crack to repair it. Determine if you want to fill it with a clear resin or if you want to mix some stone dust into the resin to create a matching color type. This is only necessary for larger cracks, as smaller ones will disappear after the clear resin is applied.
Add any stone dust if you wish and mix it together with the resin so you have a resin-infused paste. You can also apply the resin directly to the crack. Use the plastic putty knife to press the resin down into the crack from several directions so you can ensure the crack is filled. Scrape the excess off the face with the knife and then gently wipe any remaining residue up with a damp sponge or towel.
Repair the crack with a marble patch kit. The method is the same as with resin. The patch solution is applied with a plastic tool from multiple directions and then scraped off the surface so you can clean the excess film left behind.