Cotton is very sensitive to excessive water and or heat (shrinkage) I would start off with a very good detailed vacuum and dusting off with a microfiber towel. Then mix up some dry foam cleaner, and using a good clean horse hair brush work the foam in a circular overlapping motion......then vac off and towel each panel as you work, even using a hair dryer to aid in getting the cotton dry fast, to prevent spotting and water rings. If the fabric is very thin or delicate I will wipe down with dry cleaning solvent prior to dry foam cleaning, this will act like a barrier to prevent over wetting the fabric.