Colin's answer is right. Let me see if I can clarify a little bit.
First, forget that old Bernoulli explanation.
It's not wrong, but it confuses everybody.
If you create a simple symmetrical teardrop-shaped airfoil, and place it in a wind stream, then the air will flow past it, and it you turn it at an angle to the wind, it will deflect the wind stream, and it will feel a lateral force.
The vertical stabilizer of any airplane (with or without a rudder) works that way.
Now make an airplane's wings the same way - symmetrical airfoil.
Then the plane can create positive lift by tilting the nose up, and negative by tilting it down.
Some aerobatic aircraft are designed exactly that way, as in this example.
They can fly inverted just as easily as normally.
Most airplanes are not designed for inverted flight, so they use an airfoil designed for efficient upright flight, but they can still develop negative lift if called upon to do so.
(Example: The Cessna 172, a typical small plane, is stressed for 4g positive, and 2g negative.)
ASIDE: That means if the airplane, as loaded, weighs 1000kg, it is designed to withstand upward force of 4000kg and downward force of 2000kg. The latter can happen if the pilot stumbles into a downdraft at even a normal cruising speed.
Fun Fact: Inverted flight is interesting for other reasons as well.
- the ground is above you, and you have to press "nose down" to maintain altitude or climb.
- to turn left, you have to bank right, and vice-versa, because you're in negative-g.
- to turn to a heading, you have to realize that the compass is backward. If you're pointed North, East is on your left, not your right.
So it takes practice!