the back should come off fairly easy just place the moniter screen down on a towel or something else soft on the floor and undo all visable screws around the back edges of the cover. once all out try lifting it off SLOWLY and it should come off. If it gets caught on one part check for extra screws you might of missed the hey presto the back is off and ready for painting.
Now for the front, this bit is a bit more tricky. Still with the screen face down on the floor work your way around the outside of the screen itself on the inside of the casing and take out all screws that you can see are holding it in place. Once they are all out CAREFULLY try in lift the insides out of the case from underneath - ie put your hand on the front off the screen and lift up and hope the plastic stays on the floor! Again if there is any extra screws holding it in place take them out aswell and you should have all the casing off and the inside lying on you floor. put back togeather in reverse order when paint is fully hardend or you'll mark your new paint work.
WARNING DO NOT TOUCH ANYTHING ON THE INSIDES OF YOUR MONITER, THESE THINGS HOLD THEIR CHARGE AND YOU'LL GET MORE THAN A LITTLE TINGLE IF YOU TOUCH THE WRONG ONE.
DISASEMBLE AT OWN RISK.