Pick an airplane and click/press on it. In the new window, you will see a list of contracts that this plane can take on. These might be passenger contracts or cargo contracts.
Select one, and start working on it. Collect your money once the time required to complete the contract has passed. Upgrading airplanes will give you access to new, more profitable contracts.
You can find out what goods you need for fulfilling the order by clicking on the airplane at the Airport next to the City Center. Load the goods into the carriages and the plane will take off. When the airplane comes back, it will bring you construction materials.

Develop air transportation in your Megapolis!
Have fun playing the game!