If you know your oil painting has existed for a long amount of time, there is less probability of damage occurring when removing the varnish layer on a painting. If the painting was recently done within the past two to three years, you will need to be very careful about how much varnish to remove as it may affect the oils in the painting. You may want to have a professional cleaner look at it and give you a diagnosis first and ask what you can do to clean it first rather than handing it over and paying more money.
Pull together a pack of cotton swabs, cotton puff balls, any clean soft bristle makeup brushes, tweezers and a magnifying glass. Find a bowl and then spit saliva into it. While this might seem bizarre or disgusting at first glance, saliva has natural enzymes which help with digesting food. Artist Ray Smith has written that this is one of the best cleaners to use as a first step in cleaning off fire and tobacco smoke from oil paintings. The first step is to gently brush your painting with a soft bristle brush first to clear off any loose dirt.
Finish brushing the painting. Take a cotton swab, soak it with saliva from the bowl and begin wiping gently from a corner of the painting. See how it works after the first few swipes and then replenish the swab with fresh saliva from the bowl. Do not stick the swab back in your mouth for any reason. If the smoke damage is thick, you may want to do a cotton ball dabbing process with water first to see if it will loosen up the grime before using the saliva. Just lightly dip the cotton ball into water and dab it on the painting, starting in a corner. Give the water a few minutes to dissolve the grime and then try the saliva wipe with the cotton swab.
You may have to resort to added help by using mineral spirits, which are fairly odorless and can be purchased in the paint section of any home improvement store. Use a cotton ball with a light application of mineral spirits and start once again at a corner to see what happens. If the paint has been there for a while, there should be no problem with using the mineral spirits. You may have to use a lighter application on a newer painting. You should get fairly good results with the techniques provided here but it you don't, let the painting dry and then take it in for professional restoration.