A good way to experiment with this is to use your camera in aperture priority mode. In this mode, you chose the aperture, and the camera sets an appropriate shutter speed. Aperture priority is represented by an "A" or "AV" on the mode dial on the top of your DSLR camera or advanced point and shoot camera.
When Would a Photographer Use Aperture Priority Mode?
As mentioned, the primary reason to use aperture priority mode is to have control over the depth of field in a photo. For instance, if a photographer is shooting a landscape, he or she will want a wide or large depth of field to keep everything in focus. This would require an aperture of around f16/22.
But, when shooting a small object such as a piece of jewelry, the chances are that you would want a narrow or small depth of field to blur out the background and remove distracting details (such as in the photo above). This would require an aperture between f1.2 and f4/5.6, depending on how small the object was.
Mastering depth of field really improves images! Using a narrow depth of field, for instance, can help to pull a single figure or object out of a crowd.
There's nothing worse than using the wrong depth of field -- imagine a landscape shot where only the first few inches of the image are sharp!
What to Watch Out For When Shooting in Aperture Priority Mode
It's all too easy to completely forget about the shutter speed when you're concentrating on your aperture! Normally, the camera won't have a problem finding a suitable speed. But problems can arise when you want to use a wide depth of field, and there isn't much available light. This is because a wide depth of field uses a small aperture (such as f16/22), which lets very little light into the lens. To compensate for this, the camera will have to chose a slower shutter speed to allow more light into the camera.
In low light, this can mean that the camera will chose a shutter speed that is too slow for the photographer to be able to hold the camera by hand. In these cases, the most common solution is to use a tripod. If you don't have a tripod with you, you can chose to increase your ISO to compensate for the light, which will then push up your shutter speed. Just be aware that the more you push your ISO, the more noise you will end up with in your image.