Put on a dust mask and gloves. Move all furniture out of the room and strip the walls of decor, including pictures and sconces. Put drop cloths over the floor. Open the windows to improve ventilation.
Mix a mild detergent in a bucket of warm water. Place ladders in the room, and begin to clean the soot from the ceiling with sponges. It will take some effort to get the soot off completely. Rinse the sponges frequently while you're removing the soot. In some spots you may need steel wool.
Place fans in the room, and let the ceiling dry overnight.
Pour primer into a paint tray. Roll a paint roller with an extension in the tray, and begin to prime the ceiling. Make the coat thin and even. Let it dry for three to four hours, and then apply a second coat of primer. Allow to dry for another three to four hours or as long as recommended by the manufacturer.
Paint the ceiling. Rinse the paint tray thoroughly to get all the primer out. Use paint thinner if necessary. Pour a paint of your choosing into the tray, and roll on the first coat. Let dry for at least three hours, and then apply a second coat. Your sooty ceiling is now restored.