Seal around all pipes, vents and other mechanical items that broach the exterior basement walls. Use expanding foam caulk and an applicator gun.
Apply 2-by-4-inch lumber. Start with one at the top of the wall just below the point where it meets the sill plate. Attach the studs by drilling holes with a masonry drill bit and securing them with concrete screws. Put additional 2-by-4-inch studs oriented vertically running from the bottom sill plate to the 2-by-4 stud you just installed near the top sill plate. Space the 2-by-4s a distance of 16 inches apart, as measured from the center of one 2-by-4 to the center of the next.
Cut lengths of batt insulation with a razor blade utility knife that fit the wall’s height. Measure from the bottom sill plate to the ceiling joists’ bottoms. Put the insulation into the space between the studs, orienting it so the side with the paper is facing the inside of the basement. To piece together shorter lengths of batt insulation, butt the ends up against each other.
Secure the insulation between the studs by stapling the insulation backing paper to the stud about every 12 to 18 inches along the height of the wall on both sides of the strip of batt insulation.
Cut small pieces of batt insulation to insert between the ceiling joists above their bottoms and above the topmost point of the insulation you installed. Make each piece about an inch larger than the opening it fills. Do not squish down the insulation as you install it because it loses some of its insulating properties if the air spaces it contains are compressed.
Install a plastic vapor barrier on top of the batt insulation. Glue it directly to the top sill plate, the 2-by-4 studs and the bottom sill plate with construction adhesive. This keeps warm, moist interior air away from the insulation, and keeps it from encouraging the mold growth. Another method of installing vapor barrier is stapling it to the 2-by-4 studs. When using this method, overlapping cuts by about 2 feet minimizes air leakage.