Remove the drawer and carefully saw the front of the drawer from the box portion of the drawer. Saw the two sides and along the bottom, completely removing the front portion.
Sand the edges of the box part of the drawer and the back side of the front piece where it was cut away, using a medium-grit paper.
Screw hinges to the bottom of the drawer box and the drawer front so the drawer front folds down towards you.
Attach a hook and eye latch by screwing the hook on one side of the drawer box and screwing the eye in place on the front piece. Use your fingers to turn the screw or use a pair of pliers. Make certain that you line up the hook and eye properly, so the hook slides easily into the eye. This will hold the drawer front closed when not in use.
Stain the edges of the drawer box and the back side of the front piece to match the rest of the desk.