You know how sometimes plastics (like Tupperware) will get a coat of tacky/sticky stuff? (Usually grease.) Well, spray it with Windex and wait a minute or two. Then wipe it off and Whoa! Usually like new! If not do a second spray. After it is nice again, wash it in hot soapy water and rinse well.
Sometimes you see a plastic piece for sale at a thrift store or yard sale; however, someone wrote their name on it in permanent marker. Go ahead and buy it. Get home and take a whiteboard marker and go over the permanent marker. Take a rag or paper towel and wipe off both markers. You may have to do it two or three times, but it will come off.
Permanent marker on the whiteboard? Use the same ^ idea! (I have several times cleaned off whiteboards in classrooms where I am subbing.)