How do the different flaps on a plane work together to help it turn?

Answer 1

On mostly the larger aircraft, when you bank the plane either right or left the ailerons move like normal, like for a left turn the left one goes up pushing the left wing down and the right one goes down pushing the right wing up. but the aircraft is so heavy and big that it needs a little help, so along with the aileron they also move the outer flaps down a little on that wing to help push it up. they also use the spoilers on the left wing to help push that wing down. its all just enough to make the plane bank easier.

Another answer:

In order to make a proper turn in an airplane, the pilot first uses the ailerons to roll the aircraft in the desired direction. The ailerons will make the aircraft tend to yaw in the opposite direction due to the asymmetric drag they create (adverse yaw) and so the pilot will use the rudder to compensate.

Once the airplane is rolled to the desired bank angle, the pilot will then apply some nose-up pressure on the elevators to maintain altitude and press the rudder into the turn to maintain turn coordination. You can make a turn without rudder, but the aircraft will tend to "skid" (the tail of the aircraft doesnt exactly follow directly behind the nose, like sliding around a corner in the snow) which is considered very sloppy flying.

Once the turn is complete, the pilot will use the ailerons to level the aircraft, once again using rudder to compensate for adverse yaw, and providing the aircraft is trimmed for the desired attitude, release the upward pressure on the elevator.

Of course during the turn the pilot may have to make other adjustments to the aircrafts attitude using the control surfaces, such as maintaining the desired bank angle and correcting for wind gusts or air pockets.

(Additional comment to clarify good answer) Once the desired angle of bank is attained, the pilot will more or less centralise the yoke again, whilst maintaining the pressure on elevator and rudder, as he doesn't want the bank to increase any more. This is unlike driving a car when the steering wheel remains turned until the driver wants to exit the corner. A pilot will then apply opposite bank input to get the plane back straight and level again.

The questioner asks about "flaps". Since a "flap" is a specific flying control on an aeroplane, distinct from ailerons elevators, rudder and trim tabs, the question would be better put in asking about "control surfaces"