AEROPLANES FLY BECAUSE THEY GO VERY FAST
WRONG!!
Some aeroplanes go very slowly - an ex-colleague of mine designed an built one that can fly at 30 mph!(useful for spotting)
It is all about forces: aeroplanes have a WEIGHT and this is the downward pull on them. So, if you want an aeroplane to stay in the air you need an equal and opposite force UPWARDS - we call this lift.
We get lift by making the wings push air downwards and the equal and opposite reaction to the force on the air by the wing is the lift on the wing from the air. (technical stuff later).
To get lift the wing needs to go through the air, the faster it goes the more lift, so an aeroplane needs to accelerate up to a certain speed before it can take off. With a helicopter the rotor blades are just thin wings and instead of the whole aircraft moving through the air together, the rotor blades have to go at a certain speed through the air (by rotating).
If the Lift is equal to the weight then there will be no change to what is happening: ie if it is flying level it will stay flying level. If the lift is greater than the weight then it will ACCELERATE up. If the lift is less than the weight it will ACCELERATE down.
Most people assume that if an aeroplane is going upwards then the lift is greater than the weight and this is not so: this only has to be true to START it going up, once it is moving upwards if you want it to carry on going up at the same rate the lift= weight again.

Technical stuff: the principle of flight is called the Bernoulli principle: the shape of the wing cross-section is curved and as the air goes past it, it goes faster over the top than underneath because it is a bigger curve. Now Bernoulli observed that the faster the air (or any fluid) goes past a surface, the LESS the pressure on the surface: you can easily demonstrate this by holding piece of paper infront of you so it sags down, then put it next to your lips nd blow OVER THE TOP of it...the paper rises! So the moving wing has less pressure on top than underneath and this gives a resulting force UP (Lift), when the difference in pressure is great enough there is enough lift to allow the aircraft to take off. Some people don't realise that when the air leaves the back of the wing it moves DOWNWARDS to a certain extent and this gives the force. For the more technically minded: the momentum per second given to the air DOWN = the LIFT

I should also add the following (thanks to Dory): some aircraft do not have aerofoil shaped wings - especially fast jets, this is because they need very thin wings with correspondingly less drag. So how do they fly? Well, as long as they are going fast and as long as the wings are angled up slightly (we call this the "angle of attack") then the air will be forced downwards with a correponding equal but opposite force upwards on the wing. (you experience this when your hand is put outside a moving car and tilted - but DON'T DO IT ON MY RECOMMENDATION because you may be stupid enough to get your hand knocked off by an oncoming car!!!)

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