Draw over the permanent marker stains with a dry-erase marker, and then erase the marks with an eraser. This will remove most of the marks from the whiteboard, but not all of them.
Wash the whiteboard with whiteboard cleaner and a rag.
Dab a small amount of acetone on a small section of a clean rag. Do not drench the rag with acetone, as it is a harsh chemical.
Rub the acetone onto the marks using small, circular motions. Allow the acetone to completely dry. If slight marks still remain, spray window cleaner on a paper towel and wipe down the whiteboard with the paper towel.