The first time you'll find one of these will be in the Men's Locker Room (West wing, 2F). Examine it when it's in your inventory to interact with the key pad.
The objective is to press the keypad at the bottom in a sequence that turns all the lights green. If you make a mistake, all the lights will go out and you'll have to start over. There's also no set sequence for this, it's randomised each time.
The best way I found to solve it was to put dots on some paper in the shape of the lights at the top, and the keypad at the bottom. I then went left to right; top to bottom pressing each button of the keypad and marking which light it turned on with a number (top left of the keypad was 1, top right was 2, and so on)
After you've done that, just pick a starting light and follow the sequence you've laid out in an anti-clockwise direction.