In today's digital environment you can also affect exposure with ISO (the adjustable sensitivity of your camera's sensor) and and variety of light modifying options (from on- or off-camera speedlites, off-camera strobes, hotlights, reflectors, etc., etc.) and of course, some manipulation of your ambient light situation.
It is important to understand the basics of shutter speed and aperture before anything else. They not only affect the brightness or darkness of your image, but also your ability to quell motion blur, and, perhaps most importantly, depth of field, especially of backgrounds.
I just stumbled across this terrific little shutter speed and aperture simulator to give you a nice introduction to how they can affect each other dramatically. Play with it for a few minutes, trying different combinations and then get that camera in hand and go shooting!