It's the AMOUNT of light that counts
The interaction between the Aperture and the Shutter Speed determines the volume of light hitting the film. The aperture and shutter speed settings go in "opposite" directions. If you have a tiny opening, you need to have the shutter open a very long time to allow enough light in to properly expose the shot. Conversely, if you have a large opening, you need the shutter open for a short time to let in the right amount of light in to properly expose the shot.

Apertures or F-Stops
Large Opening	..........	Small Opening
f1 f1.4 f2 f2.8 f4 f5.6 f8 f11 f16 f22 f32
Shutter Speeds
Long Times	..........	Short Times
1 sec 1/2 sec 1/4 sec 1/8 sec 1/15 sec 1/30 sec 1/60 sec 1/125 sec 1/250 sec 1/500 sec 1/1000 sec

Compare this to a faucet. If you have the valve opened only slightly (a tiny aperture), the faucet needs to run for a long time (shutter speed) to fill the sink. And if the valve is opened all the way (large, or wide-open aperture), the faucet needs to run for far less time in order to fill the sink.

Suppose your meter shows that the setting you need to get the shot is f16 at 1/125sec. But you don't necessarily want to use that small an f-stop (for instance, you want to use a wide aperture to blur-out the background), or that particular shutter speed (you want a faster shutter speed to stop action).

So, if you want to use an aperture of f8, which is 2 stops open from f16 (f16 -> f11 -> f8), then you'll have to also adjust the shutter speed by the same amount of steps so your picture will be properly exposed. Here, the shutter would have to be 2 stops faster (1/125 -> 1/250 -> 1/500) Remember, the two are inversely related (if the aperture is widened - set at a smaller number, then shutter needs to be decreased - set at a larger number).

F-Stop is NOT an f-word
You might get confused about why a smaller f-stop number means a larger opening, and why a larger shutter speed number means a shorter duration. The shutter speed times are actually a fraction of a second. A speed of 1/125 (or more commonly called simply a 125th) really means 1 125th of a second. A speed of 1000th means 1 1000th of a second (a pretty SHORT duration!) So, the higher the number "seems", is really the shorter the duration. With F-stops it's the same thing. A small number like f1.4 or f2.8 really means the shutter opening is wide open. When you stop down, you are "closing down" the opening to a smaller diameter.

Reciprocity Failure
At some point in the exposure time, this relationship changes (fails). As shutter speeds get very slow (the shutter is open for greater than about 1 second) or very fast (shutter is opened for faster than about 1/1000sec), you need to make an additional adjustment to this relationship. The technical explanation for this, in a nutshell, is that when the shutter is opened for longer than it's "optimal" range, then the amount of defective electrons encountered in forming the latent image on the film is exagerated, and the film speed decreases.

The adjustment needs to made with the Shutter Speed side of the relationship. Let's say your meter reading says f22 at 10 seconds. Using the reciprocity law, the exposure would be the same at f22 and 10 seconds as it would be at f16 and 5 seconds. Let's also assume your film needs an adjustment of 1 more stop when the time reaches 10 seconds. 5 seconds is within the range of time that no compensation is needed. So if you change the aperture to f16 (which indicates a shutter speed setting of 5 seconds) and keep the shutter speed at 10 sec, you will get an overexposed image. So, if you need to use f22 (to get the depth of field you want) and and the meter shows you will need a 10 second exposure, you will need to give a 1 stop time increase to 20 seconds.

Generally, the adjustments needed to compensate for reciprocity failure is included on the data sheet that comes inside the box of film. But here are some online sources: