With the computer unplugged and turned off, wipe the computer screen gently with a dry or slightly damp microfiber cloth to clean the surface. Use a solution of one part distilled water and one part white vinegar to moisten the cloth if you need additional cleaning power.
For a few smudges, a dry microfiber cloth is often enough to tackle the cleaning job. Microfiber is soft enough that it won't scratch the screen. It also won't leave lint behind. Avoid the temptation to scrub harder on spots that don't clean easily as the pressure may damage the screen.
Once the dry cloth removes the dust and some of the smudges, add a small amount of moisture. Most cleaners are too harsh for sensitive computer screens. Any cleaners containing ammonia or alcohol can be damaging to electronics screens. White vinegar or mild soap mixed with distilled water is generally safe and effective.
Never clean a computer screen when the unit is powered on. This puts you at risk for an electric shock. If you are cleaning a laptop screen, unplug and power off the laptop. Do not spray liquids directly on the computer screen. This also increases the risk of shock and can damage the computer screen. If you use liquids, moisten the cloth and ring out any excess moisture so the cloth doesn't drip at all.