Getting the 
engine running
Place your aircraft on flat ground and right-click it to board. Most engines need fuel before they will turn over — see the fueling guide if yours is dry. Once seated, look at the engine block or press the aircraft's start control (the default is usually a dedicated key you can check in your controls menu). You will hear the engine catch and see the 
propeller begin to spin. If nothing happens, dismount and confirm the engine has fuel and that the propeller is actually attached to the engine.
Lifting off
With the engine running, apply throttle. On most aircraft you increase throttle with a forward movement key or a dedicated throttle control, and the propeller will spin faster. Hold forward pitch to tilt the nose up gently — do not yank it, or you will stall or flip. The aircraft will roll forward and then climb. Gain some altitude before turning. To steer, use your look direction or the yaw keys depending on your control scheme. Keep an eye on your altitude and speed; if the engine sputters, you are out of fuel and need to glide down carefully rather than climb.