The foil test
Tape a piece of aluminum foil tightly on all sides to the dampest spot on the wall and leave it for a day or two. If moisture forms on the room side of the foil, humid air is condensing. If it forms between the foil and the wall, water is coming through the wall. This simple test comes from University of Minnesota Extension guidance on basement moisture.
Condensation
The most common basement moisture problem and the easiest to fix. Walls and cold pipes sweat in warm, humid weather. The EPA advises keeping indoor humidity below 60 percent, ideally 30–50 percent, and insulating cold water pipes.
Seepage from surface water
Rain and snowmelt that collect next to the house soak through joints, cracks and porous block. Missing gutters, short downspouts, ground sloping toward the house and open window wells are the usual culprits. The extension guidance recommends the ground fall at least 6 inches within 10 feet of the foundation.
Groundwater leakage
When the water table rises above the basement floor, water enters under pressure through the floor and floor-wall joint. It is the least common and hardest case, and usually needs drain tile and a sump pump.

Sources: University of Minnesota Agricultural Extension Service, Correcting Basement Moisture Problems (Special Report 2, 1981); US EPA: A Brief Guide to Mold, Moisture and Your Home.