Assuming you are talking about a painting on canvas, here are some tips:
-Use a soft, dry brush to dust off the surface. You can also use a vacuum cleaner with the soft brush attachment.
-If there is dirt or grime on the surface, mix equal parts water and white vinegar in a bowl. Dip your brush in the mixture and gently scrub the dirt. Be sure to rinse the area with clean water afterwards.
-To remove mildew, mix one part bleach with four parts water. Again, use a soft brush to apply the mixture onto the affected areas. Let it sit for about 15 minutes before rinsing it off with clean water.