Despite Luftrausers referring to your vehicle as an airplane, at no point in time does it fly by means of aerodynamic lift. It's all boosters, all the time. With the Zero Gravity engine, it even drifts along in whichever way it was moving when you stop boosting.
In short, it controls much like a maneuvering space combat vehicle would: A lot of little thrusters to turn, with the main booster performing all the work. This can be hard to visualize when it's described to people, and yet here's an action packed, fun little game that approximates it quite wonderfully.