Remove the door from the hinges using a drill. Separate the sections of the door by unscrewing them if possible. Draw the desired frame size on the doors if unscrewing them isn't possible. Use a saw to cut through the door along a line parallel to the top of the door that follows the top of the desired frame. Repeat to cut off the bottom board.
Remove the side boards by cutting along the frame markings, leaving behind only a center panel. Set the center panel aside. Sand the cut edges of all four frame boards.
Run the four boards through a table saw and cut a 1/4-inch-wide groove in the center of each cut edge. Make the groove 1/2 inch deep. Leave the last inch of each end of the top and bottom boards ungrooved, but groove the entire cut surface of the side boards.
Arrange the frame boards in place and measure the dimensions of the frame opening in the middle. Add 1 inch to both dimensions of this frame and get a piece of 1/4-inch-thick glass to fit in this space. Slide the glass into the center of the frames, resting within the grooves.
Separate the boards and drill two holes into the face of each board within the area that joins up with another board, pairing these holes to make eight pairs of holes in the frame. Set a peg in each pair of holes and tighten them to see if the frame fits around the glass. Adjust as necessary. With the glass in place, apply a bead of glue to each end of each peg and along each adjoining face. Clamp the boards together around the glass. Wipe off any excess glue.
Let the glue dry overnight, then remount the door to the cabinet hinges using the same screws and a drill.