I have read the other articles on this topic and some have good information and others just are out to lunch. Let us start with the man who enabled us to fly Bernoulli. I will summarize his principle which is that as a fluid (air is a fluid) speeds up the pressure decreases. It can be shown by taking a piece of paper holding it under your lower lip and blowing. You will watch the paper rise.
How is this law important well if we decrease the pressure on the top of the wing, leaving the bottom pressure the same we will get a force upwards. This force is what all of us pilots call lift. So from looking at Bernoulli's principle we can see that if we could speed up the air going over the top and not speed up the air on the bottom we would get this lifting force. Another point to mention is that if air hits an object it tries to find a way around it. Also if two air molecules start at the same point like the leading edge of the wing they will meet at the same time (neglecting friction) at the trailing edge.
Given these two principles we can create lift. All we need to do is make the air going over the top of the wing travel a farther distance than the air on the bottom. We do this by adding camber to the wing. What is camber? Basically it is like adding a curve. This is why wings have that curve shape on the top. The bigger the curve the more lift.
Now you our thinking lets increase this curve a lot so we can generate lots of lift. Well in theory this is true except for boundary layers. There are two laminar and turbulent. There are a lot of aerodynamic principles involved with these boundary layers that limit the curve we can have to a wing which I will not bore you with.
Now there are two types of lift (of which no one so far has discussed the second type). Bernoulli lift is one type the second type is called Newtonian lift. This is based on Newton's Third Law that for every reaction there is an equal and opposite reaction.
To show this picture a wing pointed 45 degrees up (a very high attitude). The air that hits the underside of the wing is deflected downward. Since the air is deflected downward there must be an equal and opposite force acting upwards. This upward force gives you Newtonian lift. It is not a very big force but it does create some lift and I am saddened at the fact that it has not been mentioned.