To add to this guy's explanation of aperture and shutter speed:
All of your exposure values are usually measured in "stops", which represents a doubling or halving of the exposure. So if you want to maintain one exposure and go down a stop in one variable, you need to go up a stop in another.
Shutter speed stops are easy. Keep the shutter open twice as long, it lets in twice as much light. So the difference between 1 second, 1/2s, 1/4s, 1/8s, 1/16th of a second etc is all 1 stop.
Aperture is a little more confusing because the stops, for reasons of Math and Geometry and Optics, go up and down by a factor of the square root of two (which we usually just around down to 1.4). So the progression of aperture values in full stops is
1.0, 1.4, 2.0, 2.8, 4, 5.6, 8, 11, 16, 22, 32
(Since sqrt(2) * sqrt(2) = 2, you can just remember these by remembering 1 and 1.4 and then alternately doubling them up the sequence)
There are also lenses with a maximum f/stop lower than 1.0 (i.e., even larger apertures) and lenses with a minimum f/stop higher than 32 (smaller apertures).
There's also a third exposure variable you didn't mention, ISO, which is the sensitivity of your sensor/film (more or less; it's a bit fuzzy), and those also don't have a unit associated with them and you also just double/halve it to go up and down the stops. So ISO 100 to ISO 200 is one stop, and ISO 400 is one stop more, and ISO 800 is one stop more, etc.
Beyond that basic information, the best way to learn how they really work is to learn by doing. Get out there with your camera and put it in Aperture-Priority mode and pay attention to how the changing aperture changes your depth of field and changes the shutter speed you need. Put it in Shutter-priority mode and pay attention to how slow you can get the shutter speed before everything's a blurry mess. Or put it in full manual and try controlling everything by hand.