The Coanda effect is but one of several sources of lift, and not the main one. There are many, many contradictory and downright wrong explanations out there. See this incredibly informative NASA website [0] and take the Theories of Lift path. Quoting from the site, lift on a wing appears because "...the integrated velocity variation around the object produces a net turning of the gas flow. From Newton's third law of motion, a turning action of the flow will result in a re-action (aerodynamic force) on the object". In other words, wings move air "out of the way" in a specific manner, which causes a reaction force on the wing, and hence lift. That is why planes flight, other effects are secondary.
I didn't downvote you, I'm not part of that select club.
It is funny that you say "you run fast enough to make wind blow" and then you fly, because at a very simplistic level, that is exactly what is happening.
Making the wind "blow" (and not necessarily under the wing only, mind you) implies a change in velocity, which can only be the result of a change in momentum imparted by a force (the force of the wing on the air). By Newton's third law this generates a reaction force and then you get your "poof flying" moment :)
You really should read the content I mentioned, it kinda is explained all in there.
Not a downvoter, and I haven't looked at the parent comment's reference recently, but any explanation that doesn't involve forcing a parcel of air down in order to generate a force on the aircraft up probably isn't useful.
The NASA site on lift is phenomenal. Particularly the Java applet which does a simple simulation of of an airfoil with velocity and pressure plots. I've completed a specilization in Aerospace engineering, and this simulation basically sums up the fundamentals of the curriculum. The intuitive take away is the most important part, not the equations.
Fact is, objects in a moving fluid generate lift based on angle of attack. Varying the object and the fluid characteristics yields different results. Since it is a very complex system to model from first principles, it makes sense to look at real world data and simulations to develop intuition.
[0] http://www.grc.nasa.gov/WWW/k-12/airplane/lift1.html.