Pry away any existing wall paneling, drywall or other materials, leaving only the furring strips or framing, if there are already any on the wall. If there aren't any furring strips, framing or existing insulation, proceed to the next step. If there are, proceed to Step 6.
Measure the height of the wall. Cut furring strips to match the height of the wall, from floor to ceiling. You'll need one furring strip for each 24 inches of wall width.
Place a furring strip at the corner of the wall, flush against the side of the adjoining wall. Place a level along the inside edge of the strip to ensure that it's plumb. Adjust the strip if necessary.
Drill holes through the furring strip and into the blocks behind with a masonry bit. Drill a hole every 8 inches along the length of the furring strip. Insert masonry screws and tighten them until the strip is firmly attached.
Place the next furring strip 24 inches further down the wall, measuring from the center of the previous strip. Check for plumb and secure the strip to the wall. Continue mounting furring strips at a 24-inch interval until you reach the corner with the next wall. Place a furring strip here as well.
Trim rigid foam insulation panels with a utility knife and straightedge to fit between the furring strips. Apply construction adhesive to the panels and place them on the concrete block wall between the furring strips. Tape over any joints between panels with vinyl tape.
Finish the newly insulated wall with drywall, paneling or your choice of materials.