How Does An Airplane Fly?

You look up in the sky and wonder. How does an object obviously heavier than air, fly?
I bet at one point in your life you might have asked yourself that Question, especially for those of us that have a special fondness for flight. For some very curious folks like me, its one of the major reasons i made up my mind to know more and go into aviation. From there you enjoy the thrill and find your passion, you branch out to either become an air traffic controller, pilot, an engineer, a dispatcher, even doctors, lawyers and journalist can freely specialise in the industry.
These machinces suspends in the air for several hours defying the laws of gravity. Another funny fact is, airplanes come in different shapes and sizes. From very light single engine props to Heavy Jets like the 777s, 747s and A380s and let's not forget the jets design for military purposes as well as helicoptors. They are all termed "HEAVIER THAN AIR AIRCRAFTS"
Okay back to our main issue. How do Airplanes fly? Well in summary physics has the answer (that's way I indulge every wannabe pilot to take their physics lessons seriously). As for those who would become aeronautic engineers they go indept by applying mathematical theories and calculations to why an airplane flies.
There are four fundamental principles of flight
-Lift
-Weight
-Drag
-Thrust

These forces oppose each other and create a balance that keeps the aircraft in flight. I.e LIFT is opposed by the WEIGHT of the aircraft. THRUST is opposed by DRAG. These forces obeys newtons' 3rd law which states that for every action there is an equal and opposite reaction.
Airplanes
The wings of an airplane is also a major contributing factor that helps the aircraft create lift.
Example. When a B737 hurdles down the runway, air passes through the wings. From the leading edge to the trailing edge of the wings both above and below the wings. The air that passes above the wings passes with high speed and travels further with low pressure, while the air that passes below the wings of the aircraft passes at a lower speed with higher pressure. This process is what creates lift and is known as Bernoulli's principle which states that within an airflow of constant energy, when air flows through a region of lower pressure it speeds up and vice versa.
As the pilot moves his yoke towards him/her the ANGLE OF ATTACK is increased. The higher the Angle of Attack the more the pressure and the more the lift. Note that there is a degree to which a pilot can increase his Angle Of Attack. Any angle above the prescribed is know as critical angle of attack you could tilt the yolk and loose speed and enter a STALL.
Aircraft wing surface area is Dependent on the size of the aircraft. The bigger the aircraft the more thrust and wing surface area required to lift the aircraft.

For Helicopters.
I understand the basics of helicopter flight as well as its controls  movement. I had to seat on the left to have a visual comprehension, so all I know is on the surface.
 Rotor wings aircraft obey the same fundamental principles of flight. They are only different by design. Rotor heads generate lift as well as provide thrust for the helicopter. The Rotor is turned by an engine-driven shaft. Air passes through the rotor blades "just as we explained in the airplane section above" the air above the blades moves at high speeds and pushes air downward to create lift. By tilting the rotor forward, i.e pushing the cyclic forward, the downward flow is tilted backward, producing thrust for forward flight. Some helicopters have more than one rotor and a few have rotors turned by gas jets at the tips.
For a comprehensive explanation visit http://www.pilotfriend.com/training/flight_training/rotary/helis.htm