This is a quick and dirty reference piece to your camera's controls and the ways in which they affect the photographs you take. There are two controls which affect the exposure; the f/stop (or aperture) and the shutter speed.

Shutter speeds are indicated on your camera in fractions of a second, that is, 8, 15, 30 meaning 1/8th, 1/15th and 1/30th of a second. Cameras commonly go up to 1/1000th of a second and some go to 1/4000th and even 1/8000th. Although, say, 1/30th of a second sounds just blazing fast, it is comparatively slow for a camera and is probably as slow as you can hand hold the camera with your normal lens.

The crucial thing to recognize on shutter speeds is that each setting is half as long and twice as long as the adjacent speeds. That is, if your camera is set at 1/125th of a second, moving the shutter speed to 1/60th opens the shutter (and therefore exposes the film) for twice as long, whereas moving it to 1/250th of a second exposes the film for half as long. The whole sequence does that--doubling and halving as you move up and down the dial.

Note: Here's the sequence of standard shutter speeds, starting at 1 full second. Remember, each of these is twice/half as long as the adjacent shutter speeds:
 

Many cameras have manual or automatic shutter speeds slower than 1 second; some cameras have speeds faster than 1/2000th. The 1 to 1/1000th range is pretty universal although most leaf-shutter cameras (don't ask) stop at 1/500th. Also note that many modern automatic cameras will have digital displays showing intermediate speeds, e.g., 1/350th, 1/700th, etc. Don't get confused. The same rules apply--1/350th is clearly twice as long as 1/700th, but is also somewhere in between 1/250th and 1/500th.

From an artistic point of view, the shutter speed you set controls your ability to stop motion. Very fast shutter shpeeds (1/1000th, 1/2000th, etc.) can "freeze" very fast action, such as a football kickoff or child on a swing. Slow speeds (1/8th, 2 seconds) have less ability to stop motion. This isn't all bad--think of a waterfall where an exposure at 1/4 of a second invariably gives a more pleasing result than 1/500th (but use your tripod!).

The f/stop, or aperture, is the control which regulates the size of the opeing in the lens through which the light passes. The small numbers (f/1.4, 2.8) are large apertures, and let in loads of light. The large numbers (f/11, f/16) are small holes, and let in much less light. Just like on shutter speeds, each f/stop lets in half as much or twice as much light as the adjacent stops. Thus, moving from f/8 to f/5.6 (smaller number, larger hole) lets in twice as much light, whereas moving from f/8 to f/11 (larger number, smaller hole) lets in half as much light. Although it isn't as obvious from the numbers, the f/stops have exactly the same sort of doubling/halving relationship as shutter speeds have to each other. (To see this explained further, take a look at A Tedious Explanation of the f/stop to see if it clears things up a bit)

Note: Since f/stops can be confusing, here's the sequence of full f/stops. Remember, each of these lets in twice as much/half as much light as the adjacent numbers:
 

Lenses as fast as f/1.0 are extremely rare, rare enough that I've never seen one in person; not many lenses for 35mm stop down as far as f/32. Note that in the lingo, going from a wide aperture (small number) to a small aperture (larger number) and therefore letting in less light is known as "stopping down". Going the other way, and letting in more light, is "opening up".

From an artistic point of view, f/stops affect how much will be in focus in front of and behind the subject on which you actually focus. This is called depth of field. When the lens is set to a large f/stop (say, f/2.8), relatively less will be in focus in front of and behind you subject. There are times when you want to have absolutely everything in sharp focus; a small f/stop (large number) is needed for this. Other times, you'll find that throwing everything but the subject out of focus is a very good way of isolating your subject; in this case, you'll need a large f/stop (small number). Finally, there will be other times when you are fairly indifferent as to the depth of field, and in these cases, I usually use f/8 or f/11, which are the f/stops where lenses are usually their sharpest.

Now, let's tie it together. For any given amount of light and film speed, there is one correct amount of light for a correct exposure but this amount of light can be achieved with a whole series of correct exposures. This is because both the shutter speeds and f/stops double and halve. If the camera gives you an exposure of 1/125th at f/8, you can get the same amount of light to the film by setting the camera to 1/250th at f/5.6 (twice the light for half the time) or 1/60th at f/11 (half the light for twice the time) or 1/30th at f/16 (one quarter the light for four times as long), and so on. In each case, the amount of light on the film is identical; what changes is your depth of field and your ability to stop motion. This gives you creative control over how your pictures will turn out. Use it. (I have posted a handy page here to help make these relationships clearer. Take a look at this if this still seems confusing).

And don't get bogged down in the trivia. The stuff up above, once learned, is the foundation for understanding the rest of photography. It's simple for enthusiastic amateurs and equipment freaks to go off on debates about different camera brands or tripod quick release systems and try to impress you with their knowledge of filter factors. Most of it is trivia at this point. It is true that wide angle lenses have greater depth of field than telephotos, but the general rule that a smaller f/stop gives greater depth of field still applies. It is true that longer lenses require a higher shutter speed to be held steady, but the general rule still applies that a faster shutter speed has a greater ability to stop motion. It is true that films behave differently at very short and very long exposure times, but you probably won't be operating in those regions until you are at a point where you'll be ready to read about reciprocity failure and how to adjust for it. What you need to understand is above, and further knowledge will flow naturally from that and from taking and critiquing lots of pictures. So get out there and start shooting!