To ensure you get all the important letters from the public authorities when living in Denmark, it is necessary for you to get NemID.
To get NemID you will have to visit Borgerservice and remember to bring your health insurance card and passport/national ID.
Furthermore you will have to register for digital post. To do that go to www.borger.dk and use your NemID.
For more information on digital post and NemID open the PDF-file.