How can I remove a musty smell from the basement?
I think your first step is to clear out stored items and run a dehumidfier and fan in the area to drop the humidity. You didn't mention the type of walls, ceilings and floor coverings.  Normally, if you smell a musty odor, you will have some mildew somewhere. Are there fabric or paper items stored there now? if the odor still exists after drying out the area, you should thoroughly wash the floors and walls, etc. with a mild bleach and water solution and dry it out again. Depending on the wall and ceiling coverings, a coat of mold resistant paint may be required. Concrete floors may need a waterproof treatment like Driloc.