By plane:

Copenhagen Airport (CPH) 
From Copenhagen airport you can continue to Aarhus Airport by domestic flight or take a train to Aarhus.
The train to Aarhus goes from Terminal 2, connection every hour. Travel time approx. 3.5 hours. Ticket price: Approx. 400 DKK.

Aarhus Airport/Tirstrup (AAR)
Is a small airport located approximately 40 kilometers from Aarhus. There are several daily flights between Copenhagen Airport and Aarhus Airport, and a few international connections.
The airport bus goes to the Aarhus Central Train Station. Travel time 50 minutes.

Billund Airport (BLL)
Is located approximately 90 kilometers from Aarhus. It has direct flights to many major airports in Europe.
The airport bus goes to the Aarhus Central Bus Station. Travel time 1 hour and 45 minutes.