Some laptops have a physical shutter that you can toggle back and forth across the lens. Before taking a photo, check the camera lens (typically at the top-center part of the screen) and make sure the shutter is open.
Make sure to activate your camera with the proper permissions.
You should also see yourself appear on-screen in Photo Booth once the camera is on.
If you have an iPhone or iPad with Photo Stream enabled, the photo will also appear on your iPhone or iPad. You can add extra effects in Photo Booth such as a customized background.
