With many digital cameras, if you press the "take picture" button down slightly, it corrects the white balance, sets the F-stop and does other things based on what is at the center of its field of vision when you slightly press it. If you keep slightly holding the button down, it'll keep those settings without changing even if you move the camera to point at other stuff.
To wit: If you point your camera at a bright light and press the button down slightly, the camera will adjust by not taking in as much light. When you then point the camera at something darker, like a person in front of a computer screen, while still slightly holding down the button, the camera should keep that "not taking it as much light" setting. Then the computer screen won't show up as a shining beacon of whiteness, heh.
If your camera is older or has a gimped feature set, though, all of this is moot. =/