Use a soft paint brush and brush gently, try it in one corner and see how that works.

christine1950: I shall try a brush.... though I suspect it has more than just dust on the surface now over the years.I know it may be silly to try saving this cheap paper reproduction... but I have always loved it & it really is pretty... have to get up close to tell it is not a real painting & the frame is pretty also! I wonder if when I purchased it, I could have sprayed it with something to give it a permanent finish that could be cleaned .. too late for that now though!

Do you have a Hobby Lobby? in your area? or even an Art Gallery? Just be honest with the dealers and tell them it is not expensive but you do like it and want to know how to clean it. Most will help you are. Do you have college that teaches art? Some colleges have art galleries also. Check the newspapers for art shows --just some ideas Hope this helps