In the movie Little Big Man, Dustin Hoffman's character learns to draw and fire a gun. He was taught to use "snake eyes" right before pulling the trigger. I laughed out loud because it's exactly what I do when I make a photograph.
It goes like this: I wander with my eyes wide open until something interests me.
I'll size it up, try it on, decide on a point of view, figure out whether there are any technical difficulties and whether they can be overcome. Then I'll frame it up.
Now, all of this can happen in two or three seconds, but it's the last bit that's evolved into the critical instant. Once I have it framed, I almost defocus my eyes, taking everything in the frame in, all at once, checking the edges, watching the horizon level and proportions-thirds, maybe fifths(I'll get into more of a discussion on rules and breaking them later). But at the very last, after checking these things, I make a little micro adjustment when it feels just so. "Yes, yes, that's it." Click. Very important.
It really is a matter of a millimeter.