A nice little animated GIF from Wikipedia showing how the flight controls in an aircraft work. The rudder pedals and control column (also known as the control stick, control yoke or control wheel) or joystick on more modern aircraft, move the control surfaces to make the aircraft roll, pitch or yaw. A): aileron, B): control stick, C): elevator, D): rudder. In early aircraft, the linkages would have been steel cables like bicycle brake cables or car handbrake cables. This system is still used on some light aircraft. As aircraft became larger, it would have been infeasible to move heavy control surfaces by hand simply because of their weight and aerodynamic forces on the surfaces (like when you try to control an umbrella in high winds) so hydraulics was used to move the surfaces (similar to the way a digger works.) Nowadays most aircraft are fly-by-wire, meaning when the pilot moves the stick, a control signal is sent to electrical servos which move the control surfaces. The Airbus A320 was the first commercial aircraft to use this system in 1987 although fighter aircraft previously used a version of the technology. Fly-by-optics is another development, allowing higher data transfer rates and immunity to electromagnetic interference (EMI).
There's a discussion about fly-by-wire on Aviation StackExchange here.
Image attribution: Piotr Jaworski, CC BY-SA 3.0 via Wikimedia Commons. Original animated GIF converted to this MP4 video.