Lay the painting face up on your work bench. Make sure you do this project in a well-ventilated room and that you are wearing rubber gloves.
Apply neutralizer to the painting with cotton balls. This will remove the surface dirt. Apply the solution in rolling strokes rather than scrubbing it. This will keep the integrity of the painting intact.
Test your different cleaners in one corner of the painting. For yellowed varnish you'll want to use the varnish remover; if there is a lot of dirt and smoke you'll need emulsion cleaner. Right after you apply a test stroke of cleaner, use neutralizer on a new cotton ball to stop the cleaning action.
Clean the painting. Once you've figured out which cleaner to use, take your cotton swabs and roll small amounts of the cleaner over the painting. Make sure not to scrub on the painting; the cleaners should do their job without a need to rub. Once you've used the swab once, do not dip it into the cleaner again. It is suggested to use cleaner on a 2-inch patch at a time, then apply neutralizer to the area.
Varnish. Once you've cleaned up the painting, apply new varnish to it using a small paintbrush.