Nordic citizens are free to enter, live, study and work in Denmark and do not need a visa or residence permit.
EU/EEA/Swiss citizens can reside and work in Denmark according to EU special regulations and should apply for an EU residence document upon taking residence in Denmark.
Non EU/EEA/Swiss citizens must apply for a residence permit to reside in Denmark. Many residence permits include a work permit but it is important that you have the correct permit for the job in which you will be employed. You may also need to apply for a specific work permit, if you are going to do unpaid voluntary work or seek sideline employment.