Start at one end of the brick wall and measure the distance from the floor to the ceiling. Transfer this measurement to a furring strip. Cut the furring strip to the appropriate length with a handsaw.
Set the furring strip on the brick wall, with one edge lined up with the brick wall's edge. Set a level against the furring strip's other edge. Adjust the furring strip so it is plumb.
Put a 5/32-inch masonry bit into a rotary hammer drill. Drill a pilot hole through the furring strip. Switch the drill to the hammer drill setting and finish drilling the pilot hole about 1 1/2 inches into the brick. Drill a pilot hole every 24 inches down the furring strip. Drive a 3/16-inch concrete screw through each pilot hole.
Measure 16 inches down from the furring strip's edge. Place a chalk mark on the brick wall at this location. This mark indicates where the next furring strip's edge will be, so the furring strips will be 16 inches apart from center.
Measure the brick wall's height along the chalk mark and transfer this to a furring strip. Cut the furring strip to the appropriate length and attach it to the wall the same way you attached the first furring strip. Measure 16 inches down from this furring strip's edge to locate the position for the next furring strip. Continue down the brick wall's length.
Measure the brick wall's height when you reach the opposite end. Cut and install a furring strip at the end of the brick wall, even if the spacing between it and the last furring strip is not 16 inches.
Position a sheet of drywall over the furring strips on one end of the brick wall. A full sheet of drywall should span six furring strips, with the edge resting on the sixth strip's center.
Drive 1-inch drywall screws through the drywall and into the furring strips. Use a row of four drywall screws that are evenly spaced along each strip.
Position a second sheet of drywall next to the first sheet, with the edges butted up tightly together. Secure this sheet of drywall to each of the furring strips it covers. Continue until you cover the entire brick wall with drywall.