Attaching furring strips to a concrete block wall requires a special tool and specific screws. The dual action of a hammer drill makes drilling holes in block much easier, and it saves on bit wear as well. Concrete screws have a thread pattern that is designed to grip masonry. Concrete block walls, especially in basements, are notoriously out of square and plumb, so you may need to make adjustments to the strips to account for this.
Clean the blocks on the wall that will receive the furring strips. The wall should be free of dirt, loose concrete and grease.
Apply a coat of masonry waterproofing paint to help reduce moisture that can seep in through concrete. This is an optional step, but it can help to keep furring strips dry in humid basements.
Determine how the strips will be attached --- horizontally or vertically. Make pencil marks on the wall to indicate where the furring strips will be attached. Mark lines 16 inches on center, and use a level to ensure that each line is plumb or level.
Snap chalk lines across all the pencil lines to make them more visible.
Saw furring strips to the correct length for your wall installation.
Run a 4-foot level along the wall to check for low and high spots. Furring strips, when screwed in place, will follow the contours of the wall. Note irregularities by making penciled notes on the wall so you will know where these locations are as you attach the strips.
Apply a bead of construction adhesive for extra holding power. This step may be omitted if you know the furring strips might be removed in the future.
Follow the chalked layout lines you created earlier, placing a furring strip in position and making sure it is plumb or level, depending on your layout.
Drill pilot holes through the strip and into the concrete block with a special combination bit attached to a hammer drill. The bit is made to cut through both wood and concrete. Insert a concrete screw into the pilot hole and use the combination bit to screw it in. Add shims if needed where the strip crosses a low point, and use the level to make sure the entire length of the furring strip is plumb or level. Use a block plane to shave off some of the furring strip at points where it crosses high spots on the wall.
Repeat the process until all the furring strips are in place.