I used a Q-tip and fingernail polish remover. Just put a bit of remover on the end of the Q-tip, remove a small area, then wipe it off immediately with a soft cloth - I used the normal microfiber cloth that I use to clean the LCD normally. Worked great!
Glass cleaner or white vinegar,it might take a few goes,use a clean micro-fibre cloth,one that has not got any polish in it ,spray a mist of glass cleaner,vinegar, on the cloth ,not the screen wipe over the screen ,turn the cloth to a clean bit each time you wipe ,top left to right,back and forth and slowly working down. Don't use any other cloths they can scratch the surface,or spray directly on the screen.
If it is a glass CRT screen without antiglare coating, you should try nail-polish remover or acetone. If it is an LCD or any type of plastic you are probably out of luck because any chemical strong enough to remove it will be likely to damage the surface of the screen.
