Set up your step ladder so you can climb up between two joists. Sweep off each individual board of the joists with your 3-inch paint brush.
Fill your bucket with water. Add 1 tsp. of liquid dish soap to the water in your bucket. Stir the mixture with your sponge.
Wash the joists with the soapy water. Rub your wet, soapy sponge along each board to remove any visible mold. Rub with the grain of the boards. Rinse your sponge often.
Attach the handle of your box fan to the joists with tie wire. Snip the wire with your wire cutters as needed. Turn on the fan to provide air circulation to help the wet joists dry faster.
Spray the joists with fungicide. Soak each board and be sure to spray into the crevices between the boards. Let the fungicide dry for 24 hours.
Spray polyurethane onto the joists to seal them and prevent future mold growth. Let the polyurethane dry completely before removing the fan.