Run the vacuum clean over all the loose chalk dust before you begin to clean any markings from the carpet.
Wipe the chalk from your carpet with a clean white cloth that has been dipped in warm water. If you get to it quickly, this may be all you need to properly remove any markings. But in certain cases, such as with blue chalk on white carpet, you may have a stain to deal with.
Make a cleaning solution with 2 cups of warm water and 1 tbsp. of liquid dish soap. Mix them together in a bowl.
Dip a clean white cloth into your cleaning solution and repeatedly push down on the carpet with the cloth until the chalk stain is gone. You may need to rinse off the cloth and dip it into the solution again if there is a large stain.
Apply cold water to the clean area on the carpet with a sponge. Then dry it with another clean white cloth.