What is the best way to drywall a basement staircase?
With concrete, the concern is moisture.  Any furring strips should be pressure treated, and I've also seen good suggestions to use the foam barrier that you would typically use under a sill plate as an extra defense, e.g. this stuff (click the photo for the product page):



For pressure treated, make sure any nails are galvanized to avoid the chemical reaction that would eat normal nails. If you're using foam panel insulation, then seal any gaps on the sides. I'd also use a vapor barrier on top of the furring strips, behind the drywall. And finally, for the drywall, use something mold and moisture resistant to avoid future problems. Moist environments are also a good place to use the fiberglass mesh tape, instead of the paper tape, to finish the joints.