From a physicist's point of view, a wing is just a machine for producing downwash - a glorified wedge, if you like. The momentum change in deflecting the air in a given direction is what provides the "lift" force in the opposite direction - whether up, down, sideways or forwards.
Now the only way a gas can exert a force is through pressure - remember force over area? So, if there is a lift force there must be a pressure difference between the two sides of the wing.
If you then assume that the airflow is laminar and incompressible, and apply conservation of energy, you conclude that the air on the low-pressure side is travelling faster than the air on the other side - hey, you've derived Bernoulli's principle!
So much for the basic idea. In practice, most of the pressure change,and hence lift, occurs on the low-pressure side of the wing, and not, as you may expect, on the underside. This is where all the whizz-bang of streamlines, stagnation points and circulation comes in. It's not possible to explain this in simple terms, yet it is vitally important in keeping an aircraft in the air (a fully stalled wing, where virtually all the lift comes from the lower surface, can provide as much lift as an unstalled wing at a great enough angle of attack. But of course the drag is horrendous, the engines can't keep up and so gravity chips in to maintain equilibrium - AF447 in a nutshell). Hence the prevalence of Bernoulli in the teaching texts, and the resulting misconceptions from the pretty pictures.
You'll notice I haven't answered the question as to which shape provides the most lift. But then, that's just a detail
