Place the oil painting flat on a table. Put on a pair of surgical gloves because you do not want the oil from your skin tampering with the painting.
Add neutralizer to a cotton cloth and wipe the oil painting down gently. Avoid putting pressure on the painting. Neutralizer can be purchased at arts and craft stores near the paint section.
Place some emulsion cleaner on one cotton swab and some varnish remover on another. Test the two in one of the corners of the painting to see which cleans better.
Apply more neutralizer to the cotton cloth and wipe over the area you just cleaned with the varnish or emulsion cleaner. This prevents any of the chemicals from damaging the painting.
Roll the cotton swab over the oil painting gently and slowly as you clean. Once the swab is dirty, throw it away and begin using a new cotton swab.
Apply gloss varnish to the painting once you have completed the cleaning process. This will protect the painting from any future dirt or dust.