There is a whole lot of confusion here!
Firstly there is a very good understanding of how wings work, there is just heaps of overly simplified versions out there that just muddy the water.
However, it's true that when you start adding things like turbulent flow, things get trickier to culculate.
As for some in this thread thinking they nearly as much as engineers that specialise in this field peharps not, if you do abit of reseach you will find some very helpful information. The problem is there is also a lot of garbage.
For example, people often say newtons laws do not apply. Thats wrong, because air has mass so they do apply, if you deflect air in a certain direction, there will be a force upon the object in the opposite direction.
People say that it a fluid has to take the same amount of time to travel over an object as it does to travel under. This is absolutely not true.
And also it is important to understand that it is not just the shape of the wing that has an impact on the pressure difference and therefore lift. Take an airplane for example when flying inverted why do they not fall out of the sky? Because the angle of atack plays a critical role in the amount of lift, not nesicarily the shape.
And also someone refered to negative pressure, but were told they were wrong, however they were not wrong they were refering to negative pressure relative to atmospheric pressure.
Best thing to do is read up!
*edit* I found this
We have seen that several physical principles are involved in producing lift. Each of the following statements is correct as far as it goes:
1)The wing produces lift “because” it is flying at an angle of attack.
2)The wing produces lift “because” of circulation.
3)The wing produces lift “because” of Bernoulli’s principle.
4)The wing produces lift “because” of Newton’s law of action and reaction.
We now examine the relationship between these physical principles.
Do we get a little bit of lift because of Bernoulli, and a little bit more because of Newton? No, the laws of physics are not cumulative in this way.
There is only one lift-producing process. Each of the explanations itemized above concentrates on a different aspect of this one process.
The wing produces circulation in proportion to its angle of attack (and its airspeed). This circulation means the air above the wing is moving faster. This in turn produces low pressure in accordance with Bernoulli’s principle. The low pressure pulls up on the wing and pulls down on the air in accordance with all of Newton’s laws.
referance
http://www.av8n.com//how/htm/airfoils.html