Take a soft brush, such as a paintbrush, baby toothbrush or shaving brush, and gently rub the brush over the oil painting using circular strokes. This will remove undesirable particles, such as dust and soot. Note that this should not be done on any part of the oil painting that is still wet.
Fill a clean bowl with water and a few drops of dish-washing detergent.
Take a clean cloth and dip it into the bowl and then dab the cloth onto the oil painting. This will remove blemishes such as fingerprints and minor stains. It is best to try dabbing the cloth on an area of the oil painting that is covered by the frame before dabbing the cloth on the rest of the painting. This way, if the water and detergent discolor the painting, you can stop what you are doing without having caused any serious harm.
Bring the oil paining to a conservator or restorer. If you cannot clean the oil painting to your satisfaction by following the steps above or you are too concerned about damaging the oil painting, you should have a professional look at it.