Rub the paint specks with a cloth saturated with hot water. The water should be as hot as you can handle. Rub the specks off the wood furniture with the saturated cloth in a circular motion until the paint is no longer visible. If the hot water does not remove the paint specks, continue to Step 2.
Mix 1 gallon of water with 1/3 cup of TSP. TSP--trisodium phosphate--is a heavy-duty cleaner that is available at home improvement stores. Saturate a clean cloth in the mixture and scrub the paint specks off the wood furniture. Continue to Step 3 if the paint specks are still visible.
Apply turpentine to a clean cloth and rub the paint specks. Turpentine should be used in a well-ventilated area away from open flames or sparks. Turpentine may remove the wood furniture's finish and stain so use caution when working with turpentine. Wipe the wood furniture clean with a damp, soapy cloth.