An accidental ink swipe or deliberate artistic creation from your child can result in ink stains on your plastic surface. It seems you should be able to just wipe an ink stain off plastic but, since ink is meant to adhere to the surface to which it's applied, this isn't usually the case. Remove the ink stain as soon as possible before it becomes set into the plastic.
Place 2 tbsp. liquid hand dish washing detergent and 1 tbsp. rubbing alcohol in a bowl. Stir the two ingredients with a spoon until the detergent is blended into the alcohol.
Dip a sponge into the detergent solution and apply a generous amount to the ink-stained area of the plastic. If the plastic is small enough you can soak the stain directly in the bowl of rubbing alcohol and dish detergent. Let the ink-stained plastic soak for 15 minutes.
Scrub the ink stain with the sponge and soap solution. Rinse the sponge frequently so you don't transfer ink back onto the plastic. Rinse the plastic in hot water or wipe off with a clean cloth dampened with hot water.
Dry the plastic with a clean cloth. Assess the plastic to see if any ink stain remains. Proceed to the next step if there are any remnants of ink left on your plastic surface.
Dampen a clean cloth with nail polish remover. Wipe the remaining ink stain with the polish remover to remove the rest of the stain. Lay the dampened cloth on the ink stain and leave it in place for five minutes if the ink stain is particularly stubborn.
Wash your plastic surface with a drop of dish detergent and a sponge to remove the nail polish remover. Rinse with a water-dampened cloth, and then dry with a clean towel.