You've mixed your cleaning solution and you have your microfiber cloth ready. All you need to do is apply the solution to the screen and swipe away, right? Actually, there's more to it than that.
An LCD screen is part of a complex electronic device, either a television or computer, and you don't want any of that solution running down the screen and into your keyboard, controls or other places where it could wreak havoc. To prevent this kind of accident, first make sure you turn off the screen. You have less chance of damaging the screen when it's off, and a black screen will help you to see the dirty spots more easily.
Once the screen is turned off, dip your cloth into the solution or spray it onto the cloth, taking care not to use so much that it drips. Use the cloth to apply the cleaning liquid to the screen with gentle strokes moving in one direction. Try to avoid haphazard strokes across the screen and instead work your way clockwise or counter-clockwise. For the sake of your screen's pixels, don't push too hard and don't try to rub out a particularly stubborn spot by applying more pressure. Just keep swiping the soft cloth across the screen, reapplying cleaning solution if you're having trouble.
In less than five minutes, you should have a pristine LCD screen ready to dish up your evening entertainment. Your eyes will thank you for making the extra effort.