RULE OF THIRDS:
The Method Way
The rule of thirds is a method when used to frame a composition properly. The above diagram is that rule in visual format. Now for the written part.
Everything you see in a frame needs to be composed along the lines of the rule of thirds. The 4 intersection points are the areas where the eye should be drawn, but not all at one time mind you. These intersection points are where you place your point of interest for optimal composition.
The lines themselves can be used in the rule as well. The horizon line can seem boring and static if it runs directly through the middle of the frame. By adjusting the horizon line to one of the 2 horizontal lines, you can create a more visually appealing frame.

The above example is an Extreme Close up. Everything falls into place along the Rule Of Thirds accordingly to create good composition. Now onto the next step. See examples in action in the Composition tutorial.