Try this:
* Start off with a fine sandpaper, like 600 grit. Get most of the residue off.
* Next, go get a package of 3-grit emery boards from the drugstore. These can be found in the cosmetics section with nail-grooming items.
* Starting with the "roughest" grit, sand the area. Progress to the other 2 grits, going perpendicular (across) the previous sanding area.
* When you're done, *carefully* blow off any residue or grit.
* I like to use plain Colgate toothpaste as a plastic polish...it's cheap and works well.
* Once that's done, dip the piece in Future like MG said and let it sit for at least 48 hours before doing anything with it.