Fun fact: One of the weirdest things about heavier-than-air flight is that upon posting any explanation for it online, several people will tell you you're wrong. Each of them will also disagree with one another. All will have sources.

[EDIT] This also happens with the Oberth Effect.

The NASA article discusses a deliberately simplistic model that does not consider the deflection of airflow over the top of the wing, but it would be easy to overlook the caveat if you don't already know the answer. Further down the page there is a link to a correct Newtonian flow-turning model.

The Bernoulli equation is a valid description of what happens to the airflow pressure and velocity around a wing (at least at speeds well below sonic), but the problem is that it is not much of an explanation - it leaves you with something else to explain, namely the change in velocities. Attempts to do so without invoking calculus have resulted in the propagation of fallacies, such as the 'equal transit time' one mentioned above by tzs.

The "Newton's 3rd. law" explanation treats the wing and its immediate surrounding as a black box: air flows in, and exits deflected downwards, so there has been some downwards-directed acceleration. It does not address details of that process, such as why the above-wing airflow usually generates the larger part of the lift, or even how the deflection occurs, though it is fairly obvious that some sort of deflection will result from driving an inclined plane through the air.