I use a manually selected focus point when I have to. If the autofocus isn't focusing where I want it too I push the IIIII button and turn the dials to select the point of focus I want. Or sometimes when things are happening quickly, I'll focus and hold the * button or the half press and recompose.

One shot: The focus is set up to achieve focus on a half press (or the * button if that's the CF you've selected) and then it's done until you:
a) relax and half press again, or
b) take the photo

AI Servo: The focus is set up to track focus, as long as you're half pressed or * pressed (see above) the focus is constantly changing to follow (track) a moving subject.

AI focus: This is kind of a combination of both of the above. It acts like one shot until the subject (or camera) starts moving, then it switches to tracking focus.