1. Buy a loaf (two or three loaves if the painting is large) of a good doughy bread--a large sourdough works nicely.
2. On a pretty day, take the painting outdoors--or work inside on a large drop cloth--since this is a messy procedure.
3. Using dough pulled from the inside of the loaf, scrub the painting using gentle pressure. You will see the soil collect on the dough. Get a new hunk of dough as the older piece gets dirty or disintegrates. Continue this process over the entire surface of the work.
4. Using a soft bristle brush-- such as a good quality house painting brush--brush the remaining dough crumbs off the painting. Go methodically over the entire surface because the dough likes to stick and any remaining crumbs would be an enticement to insects.