I learned, in grade school, that lift was generated via the particles on either side of the wing having to reach the other end at the same time. Looking back, that indeed has no physicality to it. So what is the real explanation of how lift is generated? I've found references to Navier Stokes, but I don't know what that is. What is the best way to learn, from the ground up, why some curved object would generate a definite change in pressure? I can see the results, and I know that there is a pressure difference, but why is that pressure difference, and the two different velocities generated?
From what I've read, the force on a wing is calculated by integrating the sheer stress and pressure distribution around the surface of the wing. The net force is broken down into two components: the component perpendicular to the relative wind is called Lift, and the component parallel to the relative wind is called Drag.
EDIT: This is the book you want: http://www.amazon.com/Fundamentals-Aerodynamics-Mcgraw-Hill-Aeronautical-Engineering/dp/0072950463
You can find an old edition here: http://www.scribd.com/doc/6681202/Fundamentals-of-Aerodynamics