In many homes musty basement dampness can be a problem. The reasons for the dampness may vary, but the underlying problem is always the same – water penetration.
The first step in remedying the situation is to reduce the moisture inside the basement. 
If it is dry outside, open the air vents or windows to reduce the moisture level in the basement.
Even better is to use a dehumidifier.
Check outside:
Does the outside drainage slope away from the foundation (this includes the flower beds, they too must have a slope) are the gutters clean and draining and the water piped away from the foundation?
Splash blocks beneath the downspouts are inadequate for keeping the area along the foundation from being saturated with water, especially if there is a basement of crawl space.
In the Basement:
It will be necessary to wash down any mold covered areas with a bleach and soap solution (30% Clorox bleach, 20% Murphy’s oil soap and 50% water) to kill the mold.
Mold may be present on stored goods even if the basement appears to be dry, keep stored items away from the outside walls that may be damp.
Dehumidifiers work extremely well, removing the excessive moisture from the air. Set the dehumidifier control at about half, (50%) while keeping the temperature in the basement above 60 degrees.
As the air becomes dryer, mold will stop growing, and the musty smell will usually disappear.
If the dehumidifier does not reduce the damp or there is visible water on the walls or floor then the problem is more serious.
Assuming that the outside drainage is sloping away from the foundation, that there are working gutters with downspouts draining away at least 8 feet from the house, the next thing to look at will be the foundation walls.
Poured concrete (solid walls) are the easiest to fix, is there a small crack with water stains, these can be repaired with a polyurethane injection that seals the crack.
Concrete block can be much harder to repair and may require digging down outside and sealing the exterior. Systems that use a channel system around the base of the foundation wall or panels on the inside foundation wall do not cure the problem they just manage the water flow and should not be considered “a repair“.
Mold can still grow behind these panels particularly if the basement is heated.
If the walls have been painted it will be impossible to apply any sealant that penetrates the concrete without power washing or sandblasting the paint off the walls.
Topical sealants should not be used on actively wet walls as they will not act as a water barrier, they only work on reasonably dry walls to stop possible damp, for a lasting repair use a penetrating sealant that will bond with the concrete in the wall.
For sealant information, see Sealants in FAQ.
NOTE: Mold can pose a serious health problem, particularly for allergy sufferers.
