Inspect the concrete in the basement for cracks. Look at the wall and floor and check to see if there is a small gap.
Clean the cracks of the wall and fill the cracks with a crack repair kit. These are available at most hardware stores. Apply according to the instructions.
Seal the gap between the floor and wall using a foam backer rod. Fill the rest of the hole with an epoxy filler to seal the hole.
Waterproof the concrete floor of the basement if it is leaking using a concrete sealer. Apply according to the instructions on the label.
Seal any holes around pipes using caulk or an epoxy sealant. Fill leaking sections of windows in the basement using caulk.
Place a circular fan in the basement to improve air circulation. Do not open up the window as this may increase humidity.