I'd like to know how simple an explanation your friend gave thats was unsatisfactory. Maybe he was way off.
All CFI applicants should be able to explain such a basic concept. If the examiner asked how specifically the "Aileron" turned the plane, a proper answer would be that by lowering the aileron on the outside of the turn and raising it on the inside results in an increase in lift on the outside and a decrease of lift on the inside. This occurs due to the outside aileron increasing the camber and angle of attack on that wing. All you're doing in a turn is creating an imbalace in lift between the wings. One wing produces more lift than the other and causes a portion of the the vertical lift component to shift slightly into a horizontal component. Since you are diverting some of this vertical lift into horizontal lift, you will need to increase back pressure to maintain altitude. The back pressure is required since lift that was being generated to support the weight of the airplane has been taken away or shifted, you will need to develop more lift vertical lift to compensate for this. There is also a need to increase back pressure due in part to the increase in load factor. Load factor results when the airplane is moved from steady unaccelerated flight (straight and level as well as a constant speed climb may be consided as such). This added load factor increases the effective weight of the airplane and thus requires a greater amount of air lift to be generated in order to support this additional "phantom" weight. So this will also increase the amount of lift needed to be generated during a turn. While increasing the back pressure you are increasing the angle of attack as well which is the reason you generate more lift. You can increase lift by either increasing velocity or AOA. Here we are initally only using AOA. This increase in AOA has effectively increased drag (as a by product of lift) and so now the airplane begins to slow down due tothe retarding force of drag. In order to maintain your entry speed, a power increase is required to comepensate.
Many pilots mistakely believe that rudder is used to help an airplane turn. All the rudder does is to eliminate the adverse yaw that is created by the additonal drag created by the aileron being moved down. Oncethe controlsd are neutralized, rudder force may be relaxed unless torque is causing an yawing.
It is true that in order to make a coordinated constant speed and altitude turn you require coordinated use of ailerons, rudder, elevator and power.