Clean the concrete floor by sweeping it with a broom and then mopping it with a pH-neutral cleanser. Rinse with water, then pat it dry with a piece of cloth.
Reduce the flow of air in the room. This may be causing condensation, creating the wetness on your concrete.
Place two dehumidifiers in the room to remove the moisture from the air. Allow the dehumidifiers to work long enough to dry the floor out.
Apply three layers of masonry sealant over the concrete to seal the floor and prevent the seepage of moisture to the top of the concrete slab. Use a paint roller with an extension pole attached to spread the sealant in overlapping rows across the floor's surface. Keep each overlap to about 2 inches to ensure good coverage of the surface. Wait about an hour between each layer to allow one to begin to dry before applying the next. Allow the final layer 72 hours drying time before making use of the floor again.