Black permanent marker can be a real pain to remove. Here's the easiest and fastest way I found when cleaning permanent marker stains from around the home.
Get some Oops! Stain Remover and apply it to the permanent marker stain. This can and will remove paint, so be careful when using this product. Oops! Stain Remover is serious business.
Soak a rag in rubbing alcohol and rub onto any leftover black permanent marker stains. For more delicate surfaces, a mixture of toothpaste and baking soda can also work wonders.
Saturate the permanent marker stains with bleach and let it soak in for 20 or 30 minutes, depending on the severity of the stain. Then scrub the area with a rag to remove the stain.
Ventilate the area for a few hours, as some of these products can cause health problems if breathed heavily over long periods of time.