Like in planes, you can use the left and right mouse buttons to turn your helicopter quickly, but I find this to be more useful in a helicopter like the Mi-28 Havoc, specifically to aid the gunner (more on air vehicle gunnery later). You can predict an altitude change by the 'H' shaped heads-up display in the pilot's seat in a helicopter if the crosshairs is above the middle line, you will go higher if it is below this line, you will go lower (but faster). W will move you forward quickly, but you will experience an altitude loss shortly S will move you backward at a similar speed, but you will experience an altitude gain.
WASD controls the tilt of your helicopter, vital for moving. You also can use Mouse 1 and Mouse 2 to turn midair without flying sideways, but this ability is best used on helicopters. Also, you must keep holding the space bar to maintain airspeed. You can fly sideways, and in fact I find this to be an easy way to turn. In a plane, you use 'A' and 'D' to turn, and 'W' and 'S' to move up and down.
Now what? Aside from not crashing, this is the hard part. Alright, so now you're hovering in the air/flying forward through the air.