Since Friday's patch there has been a minor change.
Namely this part :"Once done you can pick your side in the top left (click "select army")",
Now you have to pick you side by clicking one of the flags above the playernames. Then it's the same as before, pick a white airfield and create a plane.
There was a thread from one guy who couldn't see the flags or playernames though, but the next time he connected it fixed itself. So maybe try that if you can't see the flags.
http://forum.1cpublishing.eu/showthread.php?t=24083
edit : Added screenshots to show everything visually.
Chosing a side and airbase.
Picking a plane and spawning in (creating it).
