Lay a pressure-treated 2-by-4 board in the corner on the floor with one edge pressed against the wall. Drill pilot holes through the board and into the basement's cement floor using a hammer drill and 5/32-inch masonry bit. Make one pilot hole every 16 to 18 inches.
Set the board aside. Suck out the concrete dust from each pilot hole with a vacuum. Line up the board's pilot holes with the holes in the floor.
Drive a 3/16-inch concrete screw through each pilot hole. Lay a second board on the floor. Butt up the second board's end with the first board's end and secure it in place with concrete screws. Continue until you have secured boards around the entire perimeter of the room.
Set a furring strip in one of the room's corners with the bottom edge resting on the pressure treated 2-by-4 board secured to the floor. Make the furring strip plumb in the corner using a level.
Drill 5/32-inch pilot holes through the furring strip and into the wall. Space the holes between 12 to 16 inches apart. Lay the furring strip aside and vacuum the dust out of the holes with a vacuum.
Position the furring strip back against the wall and line up the pilot holes. Drive a 3/16-inch concrete screw through each pilot hole.
Measure 16 inches along the pressure-treated board, starting from the first furring strip. Make a mark on the board. This mark indicates where to place the second furring strip so that each furring strip is 16 inches apart. Measure 16 inches along the pressure-treated board, starting from the mark and make another mark. Continue along the wall.
Set a second furring strip against the first mark you made on the pressure-treated board. Follow Steps 4 through 6 to secure the furring strips to the wall. Repeat until each mark has a furring strip against it.
Place a final furring strip against the wall's opposite corner. This furring strip may be less than 16 inches from the previous furring strip. Secure it to the wall the same way you secured the previous furring strips.