How the aircraft will turn to right side?

First, the pilot manipulates the control input, a yoke for example. Then, either mechanically or electronically, the signal from the yoke reaches the ailerons. Ailerons are the flaps usually found on the outside of the wing. Once the signal reaches the ailerons, the aileron on the right side (or left if the aircraft is turning left) lifts up. Usually, the opposite aileron will lift downwards. There other methods of banking the aircraft, but the principals are nearly all the same.