Cut the 1-by-3-inch furring strips to the height of the concrete wall. Place them on the floor along the wall 16 inches apart. You will create vertical stripes along the wall with the pieces of wood, each stripe 16 inches from the previous.
Drill holes every 24 inches from top to bottom along where each strip will go. Each hole should be about 1 1/2 inches deep. Use a carbide masonry bit on the drill to get through the concrete.
Vacuum out each hole thoroughly before proceeding. Excess debris weakens the hold between the concrete and the new wall.
Attach the furring strips to the concrete with the concrete screws. If you use screws that come with anchors, put the anchor through the wood as well to create a strong bond.
Nail the drywall to the furring strips using 1-inch drywall nails. You can use drywall screws and a screwdriver if you prefer. Then tape, mud and finish the wall as desired.