Mehran- This isn't much of an answer, but here goes.
A standard propeller-driven plane does not have enough thrust (the forward force on the plane when the engines are on) to equal the gravitational force on the plane. So pointing the plane straight up, it will fall.
Oddly, it seems that the lift force is greater than the thrust, and can exceed the plane's weight. There are two main sources of this lift. One is that the wings are curved, which causes air to move more quickly over the top than the bottom. Common descriptions of that are badly oversimplified, but the conclusion that there's lift because the Bernoulli effect makes the pressure lower in the faster-flowing air is correct. In most cases, big planes also need to have there wings angled slightly upward, which creates lift in an obvious way, since the wing is then pushing air down as it moves forward. Pitching the wings up in this manner increases the drag. This is also controllable by moving ailerons and flaps to change the shape and effective tilt of the wings.
The engines can be tilted upward too, so that there is also a vertical component of the thrust which adds to the lift.
The reason this isn't much of an answer is that I don't know how off hand how to calculate the relative sizes of these effects. The key idea is that you need a lot of surface area to generate big forces with the air, and the wings have much more surface than the propellers.
Some airplanes, particularly high-tech jets built for the military, are able to take off and land vertically, like helicopters. They have jet-engine versions and propeller-driven versions. The thrust of the engines has to be at least the weight of the plane to allow it to take off and land without a runway, and to hover. Here is a picture of a plane made by Curtiss, with engines pointing forwards and upwards for take-off.
(published on 10/22/2007)