I can't figure out how to control a plane?

You might want to wait and do that mission later in the game. Learning how to fly planes is a necessary mission later, Zero's mission are not.. so you can prolong doing them as long as you want.

If you really want the basic controls:
W is accelerate
Q and E control the rudder
Up/Down arrow control the back rudder which makes you go up and down.
And of course A, D, and the left/right arrows make you bank, hard left or right.