Summarize this article:

Removing the marker stain will be easier if you have all your materials ready and accessible before you start. You’re going to need:  A mild abrasive cleaner or enzyme cleaner. You can get these at any big box store and most supermarkets. Rubbing alcohol, also available at most supermarkets, drugstores, and big box stores. A damp washcloth. Hold a clean washcloth under running water and squeeze out the excess water. You want to make sure the spot you’re cleaning is facing up so that the cleaner doesn’t run down the surface of the wood. Make sure you cover the entire area of the marker stain. Let the cleaner sit for 2-3 minutes. Wipe in a circular motion until you remove the stain. This may take a few minutes. Rinse any remaining cleaner from the wood using a clean corner of your damp washcloth. If the stain is still there after using cleaner, soak your washcloth in rubbing alcohol. Wipe the alcohol-soaked washcloth over the stained area a few times, then rinse.

Summary:
Gather your materials. Turn the piece of wood so that the marked surface is accessible. Spray the abrasive or enzyme cleaner onto the surface of the wood. Wipe off the marker stain with a damp washcloth. Remove remaining marker with a washcloth soaked in rubbing alcohol.