You can go to Flight School in the menu to learn the controls. That said, here's a cheat sheet. Every action has several keys or buttons mapped to it, so pick the ones that feel natural:
Movement: <WASD>, cursor keys, D-pad, left stick
Change direction (helo): <DEL, END>, <Q, E>, shoulder buttons
Throttle (plane): <DEL, END>, <Q, E>, shoulder buttons
Hover (helo) | Landing mode (plane): <HOME>, <1>, select button
Move camera: <SHIFT> + cursor keys or <WASD>, right stick
Restore camera: <BACKSPACE>, <TAB>, right stick button
Cycle weapons: <PG-UP, PG-DN>, <Z, C>, top/bottom "face" button
Fire/Select: <CTRL>, <SPACEBAR>, left face button (usually X)
Lock on: <ENTER>, <ALT>, left/right trigger
Countermeasures: <INSERT>, <R>, right face button (usually B)
2x time: <\>, <~>, left stick button
Pause: <P>, <X>, start button