I purchased a sheet of standard, clear, float glass from Vision Glass (www.visionglass.com) in Springfield.  I got a 1/4" thick, 21 x 19-7/8" sheet with sanded edges.  I opted not to get tempered glass because: 1) it would have had to be ordered, and 2) the glass will be supported almost entirely on its backside by the monitor so poses little risk of personal injury.  It was just $16 and some change and was complete the end of the same day.

When I got it home, I first test fit it.  It fit just fine but it was then that I discovered my cabinet was not entirely square inside.  The top picture shows that.  After I was satisfied it was going to fit, I removed the glass and set about installing the two straight irons that were to support the glass.  These I attached to the underside of the monitor shelf, far enough out so that a small dowel can be inserted in the furthest hole to keep the glass in place.  The dowel can be seen in the fourth picture.

I then put the glass in place and taped off the screen with painters tape.  Then I laid the glass on the floor, tape-side down, and duplicated the taping on the other side.  I did this because the glass didn't sit exactly square so I could not just tape off the front and paint that.  You may get off easier.

Next I went out in the garage and painted the taped side with several coats of black spray paint.  I took my time to ensure I made even strokes to eliminate runs.  I think I put on at least eight coats.

Next came the fun part.  I installed the glass and inspected how it looked.  To be honest, I didn't think the glass would make so much difference but it really did.