The original was stapled to the wooden frame that surrounds the monitor area. Then those staples were covered with a heavy black masking tape to prevent the staples from damaging the artwork screened to the back of the bezel.
If you don't have an air stapler, you can get by with a Swingline or Powershot, but you'll probably end up setting the staples to depth with a nail punch. I recommend something short like a 1/4" staple.
Don't forget to cover the staples with a small piece of tape, black electrical tape works fine if you don't have the heavy black masking tape available.