Courtesy of Canon’s Snaphot site, here is a short infographic with the basics about how to use the rule of thirds and the golden ratio in photography.

From Wikipedia:

The rule of thirds is a “rule of thumb” or guideline which applies to the process of composing visual images such as designs, films, paintings, and photographs. The guideline proposes that an image should be imagined as divided into nine equal parts by two equally spaced horizontal lines and two equally spaced vertical lines, and that important compositional elements should be placed along these lines or their intersections. Proponents of the technique claim that aligning a subject with these points creates more tension, energy and interest in the composition than simply centering the subject.

And here is the infographic: