Most aircraft manufacturers are installing fly-by-wire control systems into aircraft now. We will cover a basic high level over-view of the components and how they work together to control the aircraft on each of the pitch, roll and yaw axis. Just going to keep it simple with primary surfaces to start.
Back in the old days mechanical flight control systems would physically link all of the surfaces to the controls in the flight deck. Pilots had hydraulic assists but nothing like what the main manufacturers in the industry are using today. Now when a pilot moves a control in the flight deck that movement is reflected in transducers within the controls whose position is read by the computers. The computers, probably installed somewhere close to the flight deck, will send the commanded position (via wiring) out to the surface. At the surface being moved there will be a component which receives the command from the computer and controls the hydraulics and actuators to move the surface.