Sorry the game is lacking tutorial in startup!
After you build ur HQ, select another airport you want to fly to and click "Plan flight" in the popup. On the right you will see dialog for setting up the route. Take note that you HAVE to purchase an airplane for that. A quick way is to choose in the dropdown the model you want (in the same screen), and click purchase in the box below it.
You can also purchase airplane via the airplane screen, which is via the left tab of the screen
HTH