First try to wipe off the marker with just plain dish soap and water with a paper towel. That should remove most of the ink. If it is not clean enough, you can try glass cleaner which should remove more ink. If you are still not happy with the chalkboard surface, try a magic eraser.
Clean a Chalkboard With Dish SoapMix a few drops of Dawn and warm water.Wet your microfiber cloth with the solution.Wipe down the board.Add additional pressure to areas with residue.Wet a microfiber cloth and rinse the board.Allow it to dry.
Start with a 70% water 30% vinegar mix and go up from there. If vinegar and water are not doing the trick try a Mr. Clean Magic Eraser. Cut it in half because unless you are erasing a very large area you won't need the whole Magic Eraser.
How to remove Washable Dry Erase Markers from chalkboard - slate or green. Wipe all stains with a damp sponge. If any stain remains, apply Soft Scrub with a damp sponge, work in a circular motion and rinse. If stain remains, saturate a cotton ball with rubbing alcohol, blot the stain and rinse.