Close-up camera views of the "denim" hanky from my reference video (see link below). Moving elements are the camera and the cloth, everything else is static. The only animation applied to the cloth is gravity and wind emitted from the floor straight up along the z axis.
The hanky is a 2x2 plane subdivided into 256 faces (16x16) and subsurfed with two render levels. Cloth settings were left at default, with a few adjustments on the "collision" tab: collision & selfcoll quality both at 2, friction at 50.
See my video "Blender Cloth Effects: Hankies, Gravity, Wind" for a side-by-side comparison of Blender's five cloth presets in action: vimeo.com/2449356