A wet basement wall may mean you have a larger problem on your hands. Water may be coming in from a variety of sources. Check for leaky downspouts or gutters that allow water to pool alongside your foundation. Blocked drainage pipes and improper grading or ruts that direct ground runoff toward your foundation are also major culprits. Correcting these problems, as well as waterproofing your basement walls, is the best way to prevent masonry surfaces from leaking.
First, determine if water seepage or condensation is causing your wet walls. Using duct tape or other strongly adhesive tape, tightly attach a 1' square of aluminum foil to an interior basement wall and leave it for several days. Remove the foil. If the room side of the foil is wet, the problem is condensation. Run a dehumidifier in your basement to help get rid of this condensation. If the wall side is wet, the problem is seepage. Note: unfortunately, both problems can occur at the same time.
Water seepage can also occur at the floor/wall joint. When concrete floors cure, they shrink and pull away from the wall, allowing a space for water to enter. You must seal all gaps between floor and walls with hydraulic cement to prevent seepage (see more on this in Step 4).