Put on eye goggles and rubber gloves to protect yourself from mold exposure.
Search for the source of moisture. If mold growth is concentrated in one area, you likely have a water leak. If there is no specific source of moisture, the musty smell and mold growth in your basement is caused by high humidity.
Fix any water leaks. If the source of moisture is not removed, mold will grow back very quickly.
Throw away any porous items, like cardboard or upholstery, that have been contaminated with mold.
Mix a quarter cup of bleach with a gallon of water and use a sponge to clean any visible mold off nonporous surfaces. Ensure that you have adequate ventilation when using bleach. Allow the bleach solution to air-dry on the surfaces.
Clean the basement thoroughly. Mold can survive on dust or dirt, so ensure that all clutter is removed and neatly organized and that the area has been swept and dusted.
Decrease the humidity in the basement by using a dehumidifier and fans.
Check the basement frequently to ensure that mold has not begun to grow back.