We use a product sold here with the brand "auto polish" its a white liquid used to remove scratches from cars. You probably have something similar in the US (I believe there's one that's a little light blue in color)... you just apply a tiny bit of the "paste" (it's neither completely liquid nor it is a paste

) in little cotton, and just buff the whole screen, trying to apply the same pressure in the whole screen so that every part is treated equally.
Please ask me if you have any more doubts, results are really amazing