The best way to remove wood varnish from your clothes is to treat the stains as soon as you can -- ideally, while the varnish is still wet. It may take several different cleaning methods to remove it, depending upon whether the varnish is oil- or water-based, but the sooner you act, the better your chances of success.
A Spot on Clothing
Remove the stained article of clothing, if you're in a position to do so, so you can access both sides of the fabric.
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Place folded paper towels under the affected area inside the clothing. Blot up wet varnish on the top side with additional paper towels. Continue blotting with fresh paper towels until you've removed as much as possible. If the varnish is dry, scrape it from the outside of the spot toward the center with the bowl of a plastic spoon.
Pour a small amount of a citrus-based cleaner or paint remover onto a white cloth or paper towel for a water-based varnish stain, or use rubbing alcohol for an oil-based varnish spot. Dab the varnish from the outside of the spot toward the center to avoid spreading it.
Rinse the spot with warm water. If the stain is still evident as the clothing starts to dry, apply a mixture of 1 part white vinegar and 4 parts warm water, scrubbing the item gently with a nylon-bristled brush. Rinse the area with warm water after a few minutes.
Treat any visible varnish with a small amount of acetone. Dab it on with a cotton swab, wiping from the outside of the spot toward the center. Rinse the area again with warm water after a minute or so.