Painting a monitor....hmm...intresting.
This should be really easy, well, from what I can think of.
First is it a CRT or LCD? CRT's are the big, bulky ones. I hope you know what an LCD screen is. LOL.
Anyway:
I would place the monitor with the screen facing you. *IMPORTANT* Cover the screen with some sort of newspaper or anything that can cover the screen if you accidently spill paint on the screen. Double goes to LCD screens. Then, I would turn it over, cover all the opening and paint from there.
I never painted a monitor before so excuse me if my intrsuctions sound like a 1st grader gave them to you. But happy painting anyways!