Cleaning an LCD Monitor takes a little more care than cleaning your traditional CRT Monitor. The old bulky CRT monitors were constructed with glass screens and could effectively be cleaned with any household material and solution that you would use for cleaning windows or glassware. Not so with an LCD screen.
You should have the monitor or the laptop turned off before you start cleaning. Apart from the safety factor, having the screen blank and dark can help highlight areas that you may have missed.

LCD Monitors use a different material for their screens and thus need a different approach to cleaning. A soft microfiber cloth is a good choice of cleaning material. An eyeglass cleaning cloth would be ideal. The LCD screens are soft and could be scratched with the wrong type cleaning cloth. Minimal pressure is a good idea too, push too hard on the screen and you could damage the crystals beneath the screens outer surface. If you can get away with a single pass using a dry cloth that is good. If not, then we need to repeat the gentle wiping or we need to add a cleaning fluid.

If you do need to use a liquid to remove stubborn spots or oily marks, consider just using water first of all. Distilled water would be best. If that doesn't cut it, then you could use a 50/50 mix of water and vinegar. Cleaning cloths should be very slightly damp, not soaked.

Here is what not to use. Don't use paper towels or kitchen towels as they could prove a little too coarse. Avoid using your fingernails. Don't use toilet tissue. Yes it is soft, but it will also break down and leave fibers in seams and gaps. Don't use household cleaning fluids. Ammonia, alcohol, acetone and chlorine are simply too harsh and may lead to damage of the screen surface. Finally, don't spray any fluids on your screen. It is highly likely that the spray will pool and run quicker than you can get a cloth to it. The end result is fluid between the case and the screen and a long dry out time.

And remember, contrary to the information provided in the movie "My Big Fat Greek Wedding", Windex does not work for everything.