Vacuum the upholstery with a hand vacuum or vacuum attachment to remove any loose soot, dirt and debris.
Sprinkle 1 cup of cornstarch over the affected upholstery. Allow the cornstarch to sit for 30 minutes to one hour before vacuuming it off. The cornstarch pulls the soot from the upholstery fibers.
Create a mixture of 1 tablespoon of liquid dish soap, 1/4 cup of white vinegar and 1/2 gallon of hot water. Dampen a kitchen sponge with the mixture, and work it into the upholstery.
Continue to work the liquid dish soap mixture into the soot stain until it is completely removed. Dampen a separate kitchen sponge with plain water, and dab at the upholstery to remove the cleaning mixture.
Press a towel against the upholstery to remove the liquid. Allow the furniture to air-dry.