Earlier quoted context omitted.
Use a clean microfiber cloth. ANYTHING ELSE will scratch your lenses up. (This is probably the most common no-no I see. People will clean their glasses with anything on them and smudge/scratch them instead.) Two cloths are ideal: one for cleaning and another for polishing. If you're using soap and water, apply a tiny amount of soap onto both sides of the lens --- less than a grain of rice --- then apply water and rub…
I don't know why people say this. When I wore glasses I cleaned them with my cotton shirts for over a decade and they didn't get scratched up, at all. I don't see how cotton would scratch glass to begin with.
To clean glasses safely you basically need a soft, clean cloth. Cotton is totally fine. You could get away with a soft clean sponge, too. Or even a soft-ish piece of paper (which is what most disposable lens words are.)