Using a router, remove the door's raised panel. Chisel out the rounded corners left by the router so right angles remain.
Sand the frame, wipe with a cloth, clean with sodium triphosphate solution, apply a stain-blocking primer, then semigloss latex paint.
Measure the opening and add an extra half inch all around. Order glass from a glass shop, choosing from clear, frosted, seeded, or ribbed glass for a unique look. Be sure to have the edges of the glass smoothed.
Place the piece of glass that has been cut to size on the back of the frame and secure it with clips. (A glass shop can do this for you or they will sell you the correct parts.)