Clean dirt, cobwebs and other debris from the bricks by sweeping the walls with a broom.
Mark vertical lines every 4 feet with a string line on the brick walls. Cut furring strips to go over the top of the string lines, making them 1 inch shorter than the height of the walls. That measurement allows you to leave a one-half inch gap at the top and bottom of the walls. Connect the furring strips to the brick walls with masonry screws and a hammer drill, placing the screws about every 10 to 12 inches along the length of the strips. These long, thin strips of wood help hold the drywall to the brick walls.
Install sheets of foam insulation between the furring strips. Apply insulation adhesive to the sheets, and press the sheets against the bricks. This waterproof insulation will help protect drywall from moisture and help the basement retain heat.
Cut drywall to fit your walls by scoring its outer paper with a utility knife and snapping off the excess drywall. Install the drywall, making the drywall joints meet over the center of the furring strips. Press the drywall closely together to create tight joints. Screw the drywall into the furring strips with drywall screws. Tighten the screws so the heads make slight dimples in the surface of the drywall paper. The indentation helps to hide the screw marks in the finished walls.
Fill the screw hole indentations with joint compound, smoothing the compound with a drywall knife and scraping off excess to create an even surface.
Apply drywall tape over the joints, and spread a thin layer of joint compound over the tape. Let the joint compound dry completely.
Sand all ridges around the drywall joints and filled screw hole indentations to create a smooth surface.