For cleaning your screen, you should use a damp (with water) soft cloth to wipe away whatever is on your monitor. This may take several repeats, but should clean your monitor just fine. Be careful to avoid dripping water down the screen; this is a wiping procedure, not a washing...
I've heard that you are _never_ supposed to clean a computer monitor with Windex which is a regular old glass cleaner. I don't know what it's made of or what the ingredient/ingredients is/are that ruins the monitor, but I guess you should just stay away from regular glass cleaners!