There's an upper rear wood door that's screwed to the back of the cabinet with black Phillips head screws (6 of them I think). Take those screws out and that upper wood door can be removed from the cabinet. The original monitor cardboard bezel is held to the back of the cabinet with flat staples. Take those staples out and throw them away. Now the cardboard monitor bezel can be 'bowed' and slip out the back of the cabinet. Now you can easily reach through and clean the rear of the plexiglass and the face of the monitor tube.
For cleaners use Formula 409, Mean Green, Fantastic, or other common household spray cleaner to get the black gunk off of there. Spray the cleaner on a soft clean towel or rag (never spray directly onto the picture tube cause the cleaner can run down inside the circuit boards) and wipe gently. Now to finish up and remove streaks use common glass cleaners like Windex.
Put the cardboard bezel back in place. Don't staple it back in place though, use thumbtacks instead. Makes it easier when you need to clean again in the future. Now put the upper back door on and tighten the screws.
