Thanks!
"One does not compose a photograph"
I disagree a little. To compose a photograph, you might reframe it, or crop it, or circle around the subject to "arrange" the elements in the photo in a pleasing way. I would consider doing this arranging 3 dimensional elements onto your 2 dimensional representation of the world.
However, I fear I'm straying too far into the academics of composition here, instead of the practical aspects (tools for making good pictures great).
My final thoughts on the subject are to learn a few of the compositional tools ('rule' of thirds, symetry, etc.), then go out and shoot with them in mind. Shoot a lot. Keep the rules that help your photos, discard those that don't. Develope your own "rules" (techniques) as well. Look at others' photos you like, and figure out what you like about them. Shoot some more. Soon you will internalize your own 'rules' and style, and it will become second nature. And the style will most likely evolve throughout your life.
How do you know when you've taken a "great" picture? Print your photo up as an 8"x10" print, or view it so that it takes up the height or width of your monitor. Look at, but don't concentrate on it. If your first thought is, "wow, that is a really cool picture!", then you probably have a great picture. If your first thought is "hey, that's kind of nice", then you have a "nice" picture. Not all pictures will be great, nor should we expect them to be. However, the ones that are both "great" AND have special emotional attachment for us (a candid shot of a child, for example) are truely special.