You don't have to worry much when cleaning old CRTs, but it's a different story with LCDs and laptop displays because they are much more delicate. You need to use a soft, non-abrasive cloth, preferably dust/lint-free, and a cleaner that's designed for use on laptop and LCD displays. You can find such at just about any local electronics or office supply store (and even Walmart) for under $5.
Spray a little onto the cloth and rub gently, but firm enough to remove the stain, whatever it is. Make sure that the cleaner doesn't run down into the cracks in the process.
How to clean stains on laptop screens ?