When clients give me computers that have lots of dirt and smudge on the screen, I grab iKlear to clean it. I saw a few years ago that it’s what Apple uses to clean laptops, especially the white MacBook prone to discoloration.
Now I also use iKlear to clean phones, tablets, and TVs. Do not to use Windex or other cleansers not specifically designed for monitors. They can permanently damage the screen. If you don’t want to spend the money, at least get a microfiber cloth and just use a small amount of plain water.