Shutter priority (S, Tv)
In shutter priority mode, you choose the shutter speed and the camera chooses the correct f-stop for that particular lighting situation. The metering is automatic, just like with Program and Aperture priority modes.
When to use Shutter priority
If you like to control motion in your photos, whether that’s blurring a waterfall, or freezing a skateboarder in midair, then choose the Shutter priority shooting mode.
Too freeze motion, you’ll need to use a shutter speed that’s faster than your moving subject. If someone is walking at a normal pace, anything faster than 1/125 second should do. If you are photographing a skier or snowboarder, then you’ll want to use a faster shutter speed. Start around 1/1000 second. If the skier is racing, then you’ll probably need to go even faster.
To blur the motion of your subject you’ll need to use a slower shutter speed. If someone is walking, try 1/30 second to start. For that snowboarder or skier, 1/60 second will definitely show motion. You may also need a tripod in case your shutter speed drops below what you can handhold.
Aperture priority (A, Av)
In Aperture priority mode, you choose the f-stop and the camera chooses a corresponding shutter speed, to give the correct exposure according to the camera’s built in meter. Again, metering is automatic.
When to use Aperture priority
If controlling depth of field is important to you, then use the Aperture priority mode.
Depth of field is: how much of your image is in focus from front to back. If you want deep depth of field, use a small aperture such as f16 or smaller. If you want shallow depth of field then use a wide open aperture like f 2.8 or larger. For more on aperture sizes, read this post.
Keep your eye on the shutter speed though, or carry a tripod with you at all times, as you may need it if your shutter speed goes too low to hand hold the camera.
Manual exposure mode (M)
In Manual exposure mode, you must set both the aperture and the shutter speed. You can still use the built in meter as a guide.
When to use Manual exposure mode
I only use Manual mode in a studio situation, when using my strobe lights (large flashes), or when doing night photography. When using studio flashes, the in-camera reflective meter does not work, so you’ll need a flash meter or some trial and error while keeping a close eye on your histogram.
In the dark, it’s hard for your meter to get a proper light reading, so manual exposure works better then too.
In all cases I keep my eye on the histogram to determine if my exposure is correct.