Cover all areas you do not want painted with painter's tape. Protect flooring with fabric dropcloths.
Apply Kilz oil-based primer to the smoke damage, using a roller frame and nap cover. Apply Kilz to areas inaccessible to the roller with a paintbrush manufactured for use with oil-based coatings. Wait four hours for the primed areas to dry.
Wash Kilz from the painting tools with mineral spirits.
Apply latex paint to the primed areas, using the clean roller, equipped with a new nap cover. Apply paint to areas inaccessible to the roller, using a paintbrush manufactured for use with water-based coatings. Wait two hours for the primed areas to dry. Add another coat if you have poor coverage.
Wash paint from the painting tools with plain tap water.