Charcoal absorbs dampness. Place charcoal in a container that has several holes in it. Place it on the floor of the area where you have dampness, a closet or larder and it will absorb the dampness.
On a larger scale you can use a de-humidifier. I have seen these machines in action and if placed in a damp room they literally remove moisture by the bucket full. Ask at your local hardware store. Be aware that they are not cheap.