Starting to look for somewhere to live as early as possible, before you arrive in Denmark, improves your chances of finding accomodation considerably. 

Some educational institutions offer help in finding accomodation for international students, so ask before trying to find a place on your own. 

StudenthousingAarhus is a collaboration between Kollegiekontoret in Aarhus, the housing organizations in Aarhus and most of the city's independent halls of residence. https://www.studenthousingaarhus.com/

Kollegiekontoret manages, maintains and modernises the 26 youth housing estates, one private and four independent hall of residences. A total of approximately 4500 tenancies.http://www.kollegiekontoret.dk/english/

AU Housing is a service for students at Aarhus University. They manage a number of rooms in different dorms housing organisations and private landlords reserved by the university. https://international.au.dk/life/locations/housing/auhousing/