Distilled Water can help you ensure that your laptop screen is spotless. Get some 2 clean cotton cloths, isopropyl alcohol, distilled water, and cotton swabs. Make sure that you never try and clean your computer screen with an old rag or paper towels using tap water or other types of alcohols as this will leave streaks and may damage your screen.
Firstly, you will need to turn your monitor off, this will help see all the dirty marks. Take one of the cloths and use it to wipe any of the loose dust off of the screen and frame, and remember not to press to hard or scrub as it may damage the screen. Then make a solution using 50/50 distilled water and isopropyl alcohol and dampen the clean side of the cloth. Gently wipe the screen from top to bottom. In order to clean the edges of the screen use cotton swabs dipped in the solution and run them along the edges while rotating them to lift out the dirt. Finally, dampen the cloth again and wipe the screen to make sure that you remove any leftover dirt from the edges.
When done, simply use the second cloth to dry the screen. Distilled water is a great way to clean computer screens and many other electronics and appliances.