BY PLANE
You can fly to Denmark via the airports in Copenhagen, Billund or Tirstrup.
As Billund Airport and Tirstrup Airport are situated close to Aarhus on the island of Jutland choosing one of these will save you a domestic flight.

Tirstrup (Aarhus)
Tirstrup is the airport closest to Aarhus; approx. 37 kilometres from the city centre. Taking the Airport shuttle to the city centre takes about 30 minutes and fares are DKK 80. Flights to Aarhus from Frankfurt and Amsterdam among other places are available on a daily basis.On flight timetables Tirstrup (Aarhus) is referred to as "Aarhus" or by the airport code "AAR".

Billund
Billund Airport is approx. 101 kilometres from Aarhus. The transport time is about 1 hour and fares are approx. DKK 150. Like Tirstrup Airport, it has daily flights coming in from Frankfurt,  Amsterdam and London. On flight timetables Billund is referred to as "Billund" or  by the airport code "BLL" 

SAS Worldwide Timetable 

BY TRAIN
You can also get to Aarhus by train. Trains from all major European cities arrive regularly at the railway station in Aarhus. 
DSB operates nearly all trains in Denmark. 

DSB Worldwide Timetable

BY CAR
Aarhus is also easily accessible by car; being situated close to highway E45 on which you can drive all the way from the German border. The driving distance from the border is about 185 kilometres and with a speed limit of 110 km/h, the drive takes less than two hours.