(A) Solid: Set the panel into a rabbet cut on the door's back and secure it with glass-door retainer clips (rockler.com) held with screws. (B) Metal mesh: Secure the panel with 3/8" x 3/8" beaded ...

Then, mount the glass using retainer clips, and finish the doors with a bead of clear silicone around the edge of the glass. Add any hardware and hang the doors. Of course, you could skip ...