Several years ago I complimented my pilots on their textbook perfect landing at LAX. They politely informed me that the computerized flight control system landed the plane quite automatically. The Wright brothers would have no clue what to do in such a cockpit. But they would recognize what the computers are controlling. The basic flight controls remain unchanged a century later.
We can compare the atmosphere to a liquid to describe how flight controls work. The rudder, in fact, controls the "yaw" axis of an airplane quite like a boat rudder does. Moving a control surface in flight will deflect air on one direction. According to Sir Isaac Newton, the object will then be forced to move in the opposite direction. Bernoulli's Principle also comes into play. The lift generated by the control surface will increase or decrease as its position is altered.
The left and right rudder pedals control the rudder. Applying "right rudder" will move the rudder into the right side airflow. This will force the airplane's tail to move left, resulting in a flat right hand turn.
Turns are better executed by also changing the "roll" axis. The ailerons, located on the outside trailing edge of each wing, control the roll axis. Turning the control wheel or yoke to the right will cause the right aileron to move up. The upward deflection of air will force that wing down. The left wing will of course do the opposite. Combining this right hand roll along with a right hand change in yaw will result in the graceful turn and bank maneuvers we are so used to.
The Elevator, located on the horizontal stabilizer, controls the "pitch" axis. Pulling back or pushing ahead the control stick will move the elevator. The pilot can pitch the nose up by pulling back on the stick. The elevator will deflect air upwards, force the tail down, and the nose up attitude will be achieved. The pilot will also have to add an appropriate amount of power to avoid stalling.
Moving the throttle lever forward increases the aircraft's power setting. Each engine will have it's own throttle lever. Propeller aircraft also have pitch and speed adjustment for each propeller. This is sometimes adjusted automatically with the throttle
The flight control system is often actuated mechanically, with wires and rods, or hydraulically. Fly by wire systems use neither - the control surfaces are actuated by electrical signals from the cockpit. These electronic systems enable aircraft to use the ultimate flight control system. Modern avionics and computers can do much more than the original autopilot. The incredible accuracy of the "auto-land" systems is actually damaging some runways by repeatedly landing planes at the same spot.
Great care must be taken when designing and maintaining control surfaces. Nearly every failure ends in tragedy. Double and triple redundancy in the flight control system is used in all areas possible.
What will flight control surfaces look like in the future? Politics are the main obstacle to completely automating flight. The three axis of flight are exclusively controlled by the ailerons, elevator and rudder. But this may change, ironically, back to the "wing warping" control of the Wright Flyer. Extremely high tech electronic/composite materials will eventually make this possible.