Slide a stud finder along the wall on either side of your bed in the general area where you would like to install the nightstands. Mark the location of each wall stud with a pencil.
Pair up the matching drawers side-by-side. Turn one drawer upside down in each pair. Hold the paired up drawers against the wall on either side of the bed with the back sides of the drawers flush against the wall. Mark the location of the studs on the drawer backs with a pencil.
Drill two evenly spaced holes through the drawer backs at each marked stud location using a drill and one-sixteenth-inch drill bit.
Hold the paired up drawers in place against the wall. Drive wood screws through the holes in the backs of the drawers and into the wall studs using a screw gun.
Unroll drawer liner into each upright drawer. Trim the liner to fit inside the upright drawers using scissors. Peel off the adhesive backing on the liner and press the liner inside the drawer bottoms with your fingers. Smooth out the liners as you press them into place.