Unscrew the hinges from the furnace room door with a screwdriver. Place the door across two sawhorses. Cut off the bottom few inches of the door with a circular saw to create a gap that allows air to vent into the furnace room. Replace the door by reattaching the hinges.
Cut out a square of drywall with a drywall saw in one of the furnace room walls. Cut out several squares, each of which is several inches wide and long, if the furnace room has appliances that require combustion air against different walls.
Place an electric box fan in one of your drywall cutouts. Plug the fan into an outlet within the furnace room. Switch the fan on whenever you use the dryer or when the furnace is under a heavy load due to very cold outdoor temperatures.
Plug in a carbon-monoxide detector within the furnace room. Test the detector regularly to ensure that it alert syou to a carbon-monoxide leak or poor drafting due to inadequate ventilation.