As a citizen from Finland, Iceland, Norway, or Sweden, you are free to live, study and work in Denmark without a residence permit.
As a citizen from the European Union, Liechtenstein, or Switzerland, or as a family member to an EU citizen, you will have to follow these steps for residing in Denmark.
As a citizen from outside the EU, Liechtenstein, and Switzerland, intending to work or study in Denmark you typically have to follow these steps when entering Denmark.
The illustration below will give you an overview of the practicalities you must attend to before moving to Denmark, when you arrive, when living in Denmark, and if you're leaving.
Do you know denmark.dk? The website, created by the Ministry of Foreign Affairs, gives you an ocean of knowledge on Danish society and culture.