The following articles explains aircraft dynamics. An aircraft can rotate around three axes: the fore-and-aft axis (or the roll axis); the spanwise (nose-up/nose-down) axis or the pitch axis; and the nose-left/nose-right, or yaw axis.
The cross-section of the wing has a shape called an airfoil. It has the property that when it meets the air (usually at some small angle, called the angle of attack) it generates an upward force (lift) for a small backward force (drag). The amount of lift (and drag) depends on the airspeed and a value called the lift coefficient (and a few other things like surface area and density of the air). If the plane is in unaccelerated flight, the upward force (approximately equal to the lift) is equal in magnitude to the weight of the plane, which is a constant. It thus follows that the total lift generated by the wing is always constant (at least in unaccelerated flight). [One example of accelerated flight is turning.]
The above mentioned coefficient of lift (abbreviated Cl) depends on the angle of attack. Usually, as the A-of-A is increased, Cl increases; to keep the lift force constant, speed can decrease. So to fly fast, we decrease Cl (and A-of-A); to slow down, increase Cl (and A-of-A). Since the wings are fixed, we alter the A-of-A by pitching the entire plane up or down. This is done with the elevator. The elevator is thus the speed control.
To turn a body moving in a straight line, a sideways force must be applied to it. For a plane, the best method for generating a force is to use the wings. To get them to act sideways, we roll the plane: now part of the lift is acting sideways and voila! a turn. To roll the plane, we use the ailerons (the movable surfaces at the wingtips). Also, notice that now since part of the lift is acting sideways, the lift force in the upward direction is reduced; but the upward component of the lift needs to be equal to the weight of the plane i.e. we need a little more lift from the wings, which we can do by increasing Cli.e. by pulling a bit of up-elevator. That’s why to turn in a plane you push the stick sideways in the direction of the turn and then pull back a bit to keep the nose level.
What happens if you try to turn with the rudder alone? The application of the rudder will cause the aircraft to yaw, and it will continue to travel in the same straight line (more or less), skidding. (Think of a car on a perfectly slippery road if you try to turn just by turning the wheel, you’ll skid but won’t turn). So we need a roll to turn.
But most of the trainers we see don’t have any ailerons! How do they turn? They use a configuration of the wings called dihedral (or, for most gliders, polyhedral).
When we apply rudder (say left rudder) to a plane with dihedral, what happens? The plane yaws; the right half of the wing then sees a greater angle of attack than than the left half:
(You can try this out if you don’t believe it: take a piece of paper and fold it slightly, like dihedral; then look at it end on, but slightly off-center, i.e. from the point of view of the approaching airflow. You will see that you can see more of the underside of one half than you can of the other.) And what does an increased angle of attack do? It increases the Cl and the lift generated by that half! So we now have the right wing generating more lift and the left less; the result is a roll to the left. With polyhedral we get the same effect, only to a larger extent.
If you try to fly slower and slower by pulling back on the stick (i.e. applying up-elevator) you will reach a point where the plane “falls out of the sky” or the stall. What happens is that an airfoil will only “work” up to a certain angle of attack. When that angle is exceeded, the airflow above the airfoil breaks up and the result is an increase in drag and a drastic decrease in lift, so that the wings can no longer support the plane. The only remedy is to reduce the A-of-A i.e. to push the nose down. This may be a little difficult to do when you see your plane fallingthe natural tendency is to pull back on the stick, to “hold the plane up.”
A development of the stall is the spin. Volumes can be written about it, and have been; go to the library and check any book on introductory aerodynamics.