I once saw video of Bob Hoover doing a barrel roll in a 19-seater turboprop while pouring himself a glass of lemonade into a glass resting on the dashboard. The glass was full as the roll ended. Cool.
Anyway, airliners and general aviation planes turn by angling the wings so that there is a lateral component of the lift that the wings produce. The more bank there is, the greater the vector of lift is angled to the side, and the faster the aircraft turns. The rudder is displaced as the ailerons are displaced, in order to counteract the extra drag on the wing that rolls upwards. (More lift = more drag, so that while banking, the wing coming up is producing more drag, and the one going down is producing less. This would tend to yaw the nose away from the direction of the desired turn.)
In general, after an aircraft is banked into a turn, some amount of aileron input is required to maintain the bank, but that's simply a question of stability.