Put on a cleaning mask and gloves before you go into your basement.
Go to the corners of your basement and look along the walls and floor for any traces of black mold. Black mold is a black substance that clings to walls and flooring. It will look like somebody has spread charcoal on your walls.
Take anything that you are storing in the basement out so you can have access to the whole room. Use a cleaner that contains bleach to kill the mold. Spray the mold down with the bleach cleaner and give it a few seconds to soak in. Use a paper towel to wipe the mold away from the walls.
Sweep the basement floor with a broom so get any dust or other mold spores off of the floor. Fill a bucket with hot water and pour a ½ cup of bleach-based cleaning solution into the bucket.
Use a mop to soak the entire floor with the cleaning solution. This will kill any remaining mold spores and help fight off the growth of mold in your basement.
Look at the pipes in your basement for any leaks. Mold grows in humidity. When a pipe leaks it creates humidity in the air and mold will form. Call a plumber to check your pipes or to tighten any connections that may be leaking.