Debian Dog
A easy way is obviously to bracket your exposures by taking several test shots.
the other more positive route to take is to meter the amount of light falling on your subject rather than reflected off the subject.
obviously this requires a hand held exposure meter with invacone in place.
I use a Sony Trinitron... just checked this with a Gossen meter, set at 800 ISO it gave me 1/15 at F1.8 ( or 1/8th at f 2.8....or 1/4 at f4 ) I transfered the setting to my 1D Mk2 and was pleased with the result .
Most important here is my reading taken at 12" from the monitor, now move away to 30" and the fall off in light intensity is considerable.
Andy is spot on, the best lens would be 50mm f1.8 or f1.4.
I'm assuming the actual monitor screen is not in shot.
if you wanted the screen with detail .
you would probably need a shutter speed of 1/80 th to 1/100 th sec because of the scanning effect on monitors & TV's. this is not an exact science, more often trial and error, but at least digital helps .
Best of luck
Martin (Huckaback Photo)
PS. a reflector just out of shot would help put a bit of detail in the shaddow side of the face.
Old photographers never die. They just go out of focus