Exposure is set by adjusting two settings; aperture and shutter speed. Between them they control the amount of light that hits the sensor (or film) when the shot is taken.
Shutter speed is fairly self explanatory, it is simply the amount of time that the sensor is exposed to light. This is usually controlled by an electrically operated mechanical shutter in front of the sensor that opens and closes very quickly for a precisely measured period of time, usually in the order of a few hundredths of a second. Obviously a shutter speed twice as long lets in twice as much light, one half as long half as much.
The aperture is also literally just that; a hole through which light passes on its way to the sensor. The diameter of that hole can be adjusted to precisely calibrated sizes. Obviously a smaller hole lets in less light, and a larger hole lets in more.
These calibrated aperture sizes, for largely historical reasons, are called stops, or f-stops. An aperture setting one stop larger lets in twice as much light. For reasons that are both historical and horribly mathematical, the standard full-stop aperture settings that you are most likely to encounter go f1.8, f2, f2.8, f4, f5.6 f8, f11, f16 and f22. Confusingly the smaller numbers refer to larger apertures, and the larger numbers to smaller ones. Many cameras can set apertures in increments of 1/3rd of a stop, but these nine numbers are the ones to remember.
Letâ€™s take an example. You set your camera to automatic, point it at a scene and take a light reading. For the sake of argument, say your cameraâ€™s lightmeter sets an aperture of f8 and 1/200th of a second. You can produce the same exposure by increasing the aperture by one stop to f5.6 and halving the shutter speed to 1/400th of a second, because this lets the same amount of light through to the sensor. Similarly, reducing the aperture to f11 and setting the shutter speed to 1/100th of a second will also produce the same exposure.
However if you alter one setting without altering the other you will change the exposure. In our example, changing the aperture to f5.6 but leaving the shutter speed at 1/200th of a second will increase the exposure by one stop, or one EV, making the picture brighter. Decreasing the aperture to f11 will reduce the exposure by one EV, making the picture darker.
Similarly, changing the shutter speed while leaving the aperture alone will also change the exposure. Double the shutter speed to 1/400th at f8 and you reduce the exposure by one stop, halve the speed to 1/100th and you increase the exposure by one stop. This is also how exposure (EV) compensation works.