Let's start with phase-detect autofocus. Here, there are a limited number of focus points to choose from. You may choose manually, in which case it doesn't pick anything -- it just tries to focus at that point.

If you chose a mode where the focus point is selected automatically, the camera will decide. Usually, this is initially based on a simple measurement, usually picking the point which has the closest focus initially as a preference. It doesn't really calculate this; each sensor gives a reading of the direction in which the focus is off and by how much, and the camera simply has to prefer the one which would give a closer focus. (In continuous or "servo" modes, the camera may attempt to track motion from one point to the next. And some advanced cameras have fancier options to tweak whether closer distances are preferred.)

With contrast detect, a similar principle applies. Here, the lens has to be moved between measurements as part of the calculation, and inherently (if you are letting the camera make the decision) the focus point choice must come after the AF movement starts. In theory, the entire sensor could be read and any area focused, but the focus algorithms tend to divide this into virtual focus point areas and then compare, narrowing down to a single rectangle to focus on. (Or, in some cases, weighing multiple areas.) On many cameras, you'll notice that CDAF is much faster if you pre-select a spot. Face detection is nice here, because if it is a face you want to focus on, the autofocus area can be narrowed down quickly without as much hunting.