Place you subject off-center
Most people place the person or object they are shooting right smack dab in the middle of the frame.
When you place your subject off center this brings into play the "Rule of Thirds"
This is a simple rule, but probably is the most popular rules. Simply, divide the image into thirds both ways. (Some DSLR cameras already have this grid available in the view finder) Then when composing your shot, place important elements either along these lines or where the lines intersect. Here's some samples:
Here is what I'm talking about when I describe dividing the frame.
On my sample images you can see that the subject is somewhere near the intersecting points. Which makes for a better composition.
Having said all of this, the rule of thirds is also one of those rules that you can break. Sometimes you might find that you prefer the subject in the center. This is just one of those basic rules that helps you to teach yourself to compose and think before you click.