For any picture if you were to place a tic-tack-toe grid over it where the horizontal and vertical lines intersect are the best spots to position the main subject of the picture. There's more to it than that but that should give you a basic understanding which is all that's needed.
This morning I was experimenting with the Rebel T2i and wanted to see if any of its 9 individual focus points aligned the a rule of thirds grid. I mounted the camera on my tripod and then one-by-one shot the same picture using each of the 9 focus points. Afterwards I loaded the images into Photoshop and added a rule of thirds grid over them.
|Simulated Rebel T2i Focusing Screen|
Am I trying to say that I'll only use 5 of the 9 focusing points on the Rebel T2i from now on? Nope, not at all. What I'm suggesting is when you want to follow the rule of thirds (and we all know rules were meant to be broken) I'll use focusing points #2, #4, #6 and #8 as the composition I'm going for warrants. I would encourage you to repeat this same sort of test with subjects you like to shoot.
Oh and for the curious all shots were taken with Donna' Rebel T2i and EF-S 55-250 lens set at 55mm. Lens and camera were mounted on the Induro CT314 Tripod. Aperture was set to f/8 and shutter speed varied, ISO 100.