There are multiple ways for doing this. Most PC monitors have 4 screw holes in the back which you can use to mount the monitor. Take a piece of wood that is as long as your cab's width and drill 4 holes into the middle, so that you can put screws through them and attach the monitor to the board. After that, you can screw the board into your cab.
Another method would be to build a wooden frame and use steel band with holes in it to fasten the monitor to it. This is what I did :

Another question I have is the black trim that seems to frame the plexi ..
That probably is black paint. You can use masking tape to mask off a rectangle the screensize of your monitor and just spraypaint the rest black. Turn the plexi over and voila ! instant plexi+bezel.
You can also do a version of the
$2 cardboard bezel or something similar to
what I did in my cab.
If you have gone the plexi+spraypaint route, you can use battens and double sided velcro to mount the plexi. You can also use a U-shaped bracket that the bottom of the plexi will slot into and something to fix it at the top.
If you build a frame for your monitor, you can make it slightly bigger than needed, mount the bezel onto it and then simply screw the plexi onto that at the top and the bottom of the frame. In my cab, the top of the frame is hidden by the speaker board, the bottom is hidden by the control panel, so no screws are visible.