With fly-by-wire and computers between pilot's command and flight control surfaces, it is easy to imagine the implementation of an autopilot inside the computer, but I read somewhere that autopilots existed before WW2. They were made only to maintain altitude and heading, but worked at a that time with the mechanical linked between pilot and control surfaces.
How did these old autopilots work?
It used a set of gyroscopes and pendulums that would correct the plane's attitude when it deviates. They were usually enhanced with pneumatic or hydraulic power to actually move the control surfaces.
For example the V-1 flying bomb (WW2 German UAV) could fly across the Channel and initiate a dive after a preset distance. It remained on course using a pendulum for pitch control and a gyroscope for yaw control. It used its inherent stability for roll control (no ailerons).
The autopilot controls hydraulic actuator that is connected to the control link at some point. Since power transfer in the link is bidirectional, the control column moves when autopilot operates it. The same goes for thrust levers operated by autothrust.
If the pilot fights it, the autopilot will increase the force applied up to some limit at which it will disconnect. It can't really recognize whether the force is from the pilot or due to aerodynamic forces, but that's all right, because it should disconnect both if the pilot tries to yank the controls and when keeping the plane in the selected attitude requires too large control input (e.g. hard up elevator because the plane is too slow).
Boeing aircraft maintains this behaviour even on models with fly-by-wire (B777 and B787). Airbus did remove the feedback, because the command given does not directly correspond to control surface position anyway. So far I believe the only other civilian aircraft without feedback is Sukhoi Su-100.
how mechanical autopilots work.
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In airplanes without hydraulic actuators on the primary flight surfaces an autopilot usually consists of servos and a computer. The servos lock onto the cables that control the primary flight surfaces. When the autopilot moves the cable you can visibly see the control yoke move the proper amount. It is not fast and will not cause damage.
The computer is monitoring the pitot/static instruments through the associated air data computer and the gyroscopic instruments through the associated attitude/heading reference system. Through algorithms, the autopilot computer controls the airplane.
