Place the reclaimed drawers on a work surface. Sand the surface of each drawer lightly with a fine-grit sanding pad in the same direction as the wood grain.
Wipe off the sanding dust with a tack cloth. Brush an even coat of primer onto each drawer with a paintbrush. Allow the primer to dry for at least four hours.
Paint the drawers with two even coats of paint using a paintbrush. Allow the paint to dry for at least four hours between coats. Let the last coat dry for 24 hours.
Slide a stud finder across the wall where you plan to mount the drawers. Mark each stud location onto the wall at the desired height for the floating drawers with a pencil.
Center each drawer between two wall studs with the bottom of the drawer flat against the wall. Orient the drawer front on the top, bottom or sides based on your aesthetic preference. Drive two evenly spaced pan head screws through the drawer into each wall stud using a screw gun to fasten the drawers to the wall.