[Fat Charlie]

It's pretty much the standard that people get taught. I'm not contesting its inaccuracy, it's just what I've always seen presented as fact. A quick google shows how ingrained the "fact" is.

Howstuffworks: How Do Airplanes Fly: Weight and Lift

As for the actual mechanics of lift, the force occurs when a moving fluid is deflected by a solid object. The wing splits the airflow in two directions: up and over the wing and down along the underside of the wing.

The wing is shaped and tilted so that the air moving over it travels faster than the air moving underneath. When moving air flows over an object and encounters an obstacle (such as a bump or a sudden increase in wing angle), its path narrows and the flow speeds up as all the molecules rush though. Once past the obstacle, the path widens and the flow slows down again. If you've ever pinched a water hose, you've observed this very principle in action. By pinching the hose, you narrow the path of the fluid flow, which speeds up the molecules. Remove the pressure and the water flow returns to its previous state.

As air speeds up, its pressure drops. So the faster-moving air moving over the wing exerts less pressure on it than the slower air moving underneath the wing. The result is an upward push of lift. In the field of fluid dynamics, this is known as Bernoulli's principle.

Howstuffworks: Aerial Navigation: Wings, Slats and Flaps

First, let's consider the angle of attack, the angle that a wing (or airfoil) presents to oncoming air. The greater the angle of attack, the greater the lift. The smaller the angle, the less lift. Interestingly enough, it's actually easier for an airplane to climb than it is to travel at a fixed altitude. A typical wing has to present a negative angle of attack (slanted forward) in order to achieve zero lift.

And here's a page from Macaulay's The Way Things Work: