With CNC, everything is run by a computer using a language (I was taught) called G-Code. It's only purpose is CNC.
For all of these parts, there's a point of reference, 0 X 0Y and 0Z for Mills (Pics 4, 5, and last 2), and 0X and 0Z for Lathes (all Others). When you know the dimensions/shapes of all your cutting bits, either the programmer writes the code from scratch (Generally results in faster manufacturing) or a Design program like Mastercam can do it for you.
CNC machines have lots of motors and feedback sensors so that it can control how the tool travels (Same principle that enables 3D printing to happen).