Shutter speed: How fast should you be going?

The shutter speed setting of your camera is what I believe is going to be the primary means of control. The shutter speed determines how long (or short) the sensor or film is exposed to what you're trying to take a picture of.

By increasing the length of exposure, you increase the amount of light going through your lens and hitting your sensor. The longer the shutter is open for, the steadier the camera is going to need to be held.
A good rule of thumb to go by in regards to stable hand-held shutter speeds is:

 1/Focal Length (mm)

 So, if you're shooting at a 50mm focal length, the slowest shutter speed that you should be using is 1/50s. With an Optical Stabilization system (IS for Canon), you can often shoot at much slower shutter speeds comfortably hand-held. I find that I can shoot at 50mm with IS enabled at a shutter speed of 1/10 comfortably and even slower with some steady breathing. Without IS enabled, I find that my slowest hand-held shutter speed is limited to 1/30.

The easiest way to test at which speed range you can comfortably take pictures hand-held is to find an object in the house that isn't moving with appropriate lighting to be perfectly exposed at shutter speeds around 1/10 and 1/30.

Higher shutter speeds are essential to freezing movement using ambient lighting. Water spray, ball movement and jumping subjects come to mind.

While it's easy to get a higher shutter speed (increasing ISO or using flash), in direct light it can be very difficult to achieve a slower shutter speed; this is where aperture comes in to play.