Like any good casual game,
Airport Mania has the balance of procedure, time management, and decision making. First things first. The main focus of the game is to get your airplane landed, offloaded, reloaded, and on its way as quickly as possible. The key to keeping the plane happy is doing the above as quickly as possible so that the plane can be on its way again. Make a plane angry and it will leave you a negative rating.
The procedure is as follows: a plane circling your airport needs a place to land. You choose the plane you wish, and then instruct it to land on one of the runways. From the runway, it has two places it can go. If there is an open terminal, it can go straight to it if you want or it can be moved to a layover spot so your runway can be clear for another landing. Once at the terminal, your plane will begin to unload. Once you have offloaded the passengers, your plane will begin to load passengers if it doesn't need anything else. Planes may require fuel or repair and will tell you what they need. Once that need has been met and the plane is back at the terminal, it will then reload and look for permission to leave. Let it know which runway it is allowed to use and off it goes. This is easy with just one plane, but try ten.
So what do you need in an airport? The terminal, the runway, and a layover spot will get you started. As you progress through the game, you will receive other tasks like fueling and repairs to juggle. As planes land and take off, depending on how they were serviced, you will receive money. This money will go towards the purchase of upgrades for your airport to make it faster and more efficient.