This page will be updated frequently with further and more detailed information.
Tirstrup Airport is about one hour from Aarhus by bus or taxi. Map: http://www.openstreetmap.org/#map=12/56.2916/10.6507.
Shuttle busses to Aarhus run on almost hourly schedule. Look for route number 925X when you are travelling with the airport shuttle. You can check the airport shuttle schedule here: https://www.midttrafik.dk/koereplaner/lufthavnsbusser-%28airport%29/aarhus-airport-%28uk%29.aspx
Billund Airport is about two hours from Aarhus by bus. Some international flights: http://www.bll.dk/?sc_lang=en
Copenhagen Airport is about three and a half hour by direct train leaving hourly during day time. Travel time is approximately 4 hours.
You can use the Danish travel planner (http://rejseplanen.dk): http://www.rejseplanen.dk/bin/query.exe/en. You can buy tickets on the page as well. we recommend that you buy tickets before you leave. The seat reservation is actually quite cheap, so if you mis your train then you can just jump on the next train from the platform.
Its possible to buy tickets in the airport. After passing customs office just continue ahead. There is a counter where you can buy tickets. Just ask for train tickets with seat reservations. The prize is approximately DKK 382,00 per person each way.
The platform is just behind the ticket counter in the airport.
Important: even though Tirstrup and Billund are the closet airports to Aarhus, sometimes it is easier and much cheaper to travel to e.g. London, Amsterdam, Hamburg and then take a fligth from there. Also Copenhagen + train to Aarhus is often easier due to the many more connections to Copenhagen and the trains leaving from CPH Airport in a frequent interval.
Its possible to go by bus from the airport in Copenhagen directly to the city center in Aarhus: http://www.abildskou.dk/en/
Travel time is between 4 and four and a half hours. This is the cheapest way to go from Copenhagen to Aarhus.
Trains from Germany, Norway and Sweden are possible. Please contact your local ticket provider.
If you need to take a train or a long distance bus please visit DSB's website http://www.dsb.dk/om-dsb/in-english/ for general information and use a great tool for planning your travel, (which can also be downloaded as an app) - the Travel Planner, http://www.rejseplanen.dk/bin/query.exe/en for all kinds of transportation and how to get from A to B in Denmark.
Local transportation within the city is by bus. Aarhus has a great system of busses. Please note that taxi is quite expensive to use and is only recommended if travelling during late night.
Local transport: https://www.midttrafik.dk/in-english.aspx
The Travel Planner is also a great tool for taking the local busses: http://www.rejseplanen.dk/bin/query.exe/en.
Other alternatives are also the city bikes, which are possible to use at various locations around the city.