Make sure your laptop is turned off and unplug the power adapter and battery. Cleaning a screen that's in use can result in permanent damage, so to be on the safe side, shut your laptop down, don't just put it to sleep. Interfering with any pixels while they're still firing could mean big problems for your laptop further down the line. Turning off the laptop will also allow you to see dirt, dust, and grime better because you're working with a dark surface. Get a microfiber cloth. These are made from a type of fabric that doesn't leave lint, in addition to being very soft. If you use a paper towel, toilet paper, T-shirt or another type of cloth, it will leave tiny particles on your screen and could even scratch it.