The game has an auto-takeoff mode that should be enabled by default. When you spawn on the runway, look for the auto-takeoff message in green in the middle of your gunsight. If it is on, then don't touch the controls and just throttle up. It should take off for you.
Otherwise, you need to apply power more slowly and allow speed to build up. The speed will put more air over the control surfaces and allow you to better control your plane. Don't jam the throttle full on right away.
Give that a try. The auto-takeoff thing is nice but it disables the second you touch the controls. Some people tend to grab the controls the second they spawn and it turns it off.
-Soda
AH Trainer Corps.