Leans cleaning cloth. I bought a pair of sunglasses (smiths) and giant headphones (skullcandy).. They both came with carrying cases made of the material, that's what I use for any glass/screen surface. It has a super high thread count making it very soft and doesn't scratch.
I bought a kit at a computer store that is meant for cleaning things like iPads and iPhones. It comes with a small bottle of spray, a microfibre cloth and some brush thing (which I don't use). Turn off your Cintiq before spraying the solution on it.