If you are flying into Denmark you have the option of four airports which all offer distinctive advantages and disadvantages. Because Denmark is such a small country, we recommend that you use a flight searching service like Skyscanner or Momondo: your main priority should be getting good flights. Using Google Maps for planning public transportation after landing is a great idea, but some of the airports might also offer specific airport busses. Check out the links below.

The closest is Aarhus Airport (AAR) which has very few flights in and out - it does feature an airport bus that will take you through the northern part of town and to the central station. Timetables are available here. Transit time to Aarhus city about one hour. 

The second closest airport is the somewhat bigger Billund Airport (BLL) which might feature more flights in and out. It is also quite remote but has busses that go to the central station in Aarhus. Timetables are available here. Transit time to Aarhus city about one hour. 

The third option is flying into Copenhagen Airport (CPH) - while a somewhat longer trip after landing, this airport is Denmark's most active and will have more connections. The best option here is to take the train directly from the airport to Aarhus. Tickets can be booked through the Danish national train services here. Alternatively you might find convenient flights from Copenhagen airport to the Aarhus Airport.

Last we have the northern airport Aalborg (AAL) which has the advantage of being located among the main train line through Denmark. While not as big as Copenhagen, it still offers good connections to larger European airports such as Frankfurt International airport. Bus and train information are available here - note that you have to take an airport bus to the main station if you do not rent a car.