Measure the height of the interior cinderblock walls in the house. Cut rigid foam panels to match the height by scoring them with a utility knife and snapping off the excess material.
Apply construction adhesive to the back of a rigid foam panel. Place the panel on the corner of a wall. Continue applying panels to cover the entire interior wall. Cut sections of panels out with a utility knife to make the panels fit around doorways or other breaks in the wall.
Hold a furring strip to the panel-covered wall at 16-inch intervals. Drill through the furring strips and the panels and into the blocks every 8 inches along the furring strips. Insert screws into the holes in the furring strips and tighten with a screwdriver to hold the furring strips snug to the wall.
Place drywall panels onto the rigid foam panels and attach them to the furring strips with drywall screws. Cut the panels to size as necessary with a sharp utility knife.
Place drywall tape onto the seams of the drywall panels. Apply drywall joint compound over the tape with a wide taping knife. Let the joint compound dry, then sand smooth with sandpaper wrapped around a sandpaper block. Clean the wall with a damp rag and you're ready for primer and paint.