Step 1: Acquire a microfiber cloth. There are many out there, but those specifically designed for glasses or lens cleaning work best.
Step 2: Shut down your laptop. Not only is it safer this way, but having a blank screen can help you see any dust that needs to be removed.
Step 3: Pressing gently on the display, wipe in one direction. Don’t scrub or wipe in circles, as this could damage the display or just move the dust particles around.
Step 4: Continue wiping across the display until it’s dust-free.
For Dirt and Grime
Step 1: Shut down your laptop and unplug it from its power source. If possible, you should also remove the battery.
Step 2: Wet the sponge with the distilled water and wring it out so there are no drips.
Step 3: Gently wipe the affected area of your monitor’s screen with the sponge. Watch for drips and clean them up immediately if there are any.
Step 4: Once the area is clean, wait for the display to completely dry out before closing the lid and/or using your machine.
For Oils and Sticky Stuff
Step 1: Shut down your laptop and unplug it from its power source. If you can, remove the battery just to play safe.
Step 2: Spray or apply the cleaning fluid onto a microfiber cloth. Make sure that the cloth is damp, but not wet.
Step 3: Gently rub the cloth over the affected area. Rub in small circles to avoid streaks and avoid heavy pressure as that can damage the display.
Step 4: Repeat as necessary, making sure not to drip any fluid onto your laptop’s display or keyboard.
Step 5: When finished, wait for the display to dry completely before closing the lid or powering on your laptop.