How do I obtain the 72 hour transit visa in Beijing airport? Is it just a matter of asking for it at passport control?

Before you board the plane, you should tell the airline company that you need to apply for the 72-hour visa free and then the airline will help you to handle your information to the airport.
Upon you reach the airport, you can get the related documents at the immigration.
Upon arrvial, you can follow the direction boards to make the process easily.