This step is one of the easier steps to perform. So grab a good flashlight andtake a stroll. I am breaking this down into three steps. It is better if you perform each step independently. It is easier to stay focused so you do not miss anything.
Ceilings: Most people understand ceilings. They should be dry, free of cracks and discolorations. Common problem areas are under bathrooms, kitchens and laundry area. Of course leaks here would generally indicate a plumbing leak or simply a one-time spill. Second main area needing specific attention is along exterior walls. Discoloration in this areas tend to be the result of condensation in the attic as a result of poor ventilation. Ice dams can also cause this but ice dams are nearly always caused by poor attic ventilation.
Wall: Some of the problems you may have found on the ceilings may extend down the walls. Damage on the walls near the ceiling on exterior walls again are the result of attic condensation. The next area of concern while inspecting the walls would be under and around windows. Signs of water such as water stains on the underside of the top trim of the window, check to see if the window is near the roof overhang. If so, the source of moisture is often the result of attic condensation. If the window is more the a couple feet below the roof line the leak is likley the result of missing or deteriorated caulking, or missing/incorrect flashing. In either case investigate further.
While walking around the home in a systematic fashion, inspect under sinks for plumbing leaks. PLEASE NOTE: Often time leaks in this area are slow and intermittent. However, that can cause a great deal of damage over time. Look closely corrosion on the pipes of for stains on the cabinet and back wall. These types of leaks are generally inexpensive to repair but very costly if ignored.
Floors: Basement floors should be inspected for moisture along the outside walls. If the area is carpeted try to pull back a small area especially outside corners. If the carpet tack strip is black or discolored there is a moisture and potential mold issue. Investigate. If you have a wood or laminate floor, watch for buckling or cupping. Either of these are the result of moisture.
Check the floor around the furnace and hot water heater. Again water in these areas may indicate a failing hot water heater or problems with the condensate drain on the furnace.
Main and upper level floors should be given special attention under the windows. Again, if the area is carpeted try to pull back small area to see the carpet tack strip. Look for discoloration.
Of course, if you find signs of moisture in any of these areas have it investigated further. If not corrected, it will ALWAYS lead to more costly repairs down the road.