The only way to fix the problem permanently is to Seal the exterior of the foundation and installing a draintile and sump system.
Running a dehumidifier is very important to reduce the humidity level in the basement. Buy a dehumidifier with an internal pump and hose. This type you can run the hose to a floor drain or sink drain and it will run continuously and drain its self.
If this is an old home where the basement is used for storage only, you can do a few things to prevent mold growth. First dispose of anything that you don’t want any longer. Throw away cardboard boxes, and organize. If you are determined to store things in the basement use plastic shelving and plastic storage totes that seal. Then you can use soap and water and wash everything in the basement. This will prevent the mold issue. You want to keep the basement as dry as possible, clean as possible, and remove surfaces that mold could grow on. (such as cardboard boxes, etc.) The key to prevent mold growth is Dry and Clean.