1. Nordic citizens
Citizens of Finland, Iceland, Norway and Sweden are free to enter, reside, study and work in Denmark. They do not need a visa, residence or work permit.
For more information:
http://www.nyidanmark.dk/en-us/coming_to_dk/eu_and_nordic_citizens/nordic_citizens.htm
2. EU/EEA or Swiss citizens
Citizens of an EU country, an EEA country or Switzerland must apply for a certificate of registration at the Regional State Administration.
For more information:
http://www.nyidanmark.dk/en-us/coming_to_dk/eu_and_nordic_citizens/eu-eea_citizens/residence_in_denmark_for_union_citizens_and_eea_nationals.htm
http://www.statsforvaltning.dk/site.aspx?p=4176
3. Third country citizens (non EU/EEA citizens)
Third country citizens must apply for a residence and work permit at the Danish Immigration Service. The application can be submitted at the Danish diplomatic mission in the country of origin of the applicant (or the country where the applicant have resided legally for the past three month). The mission will then forward the application to the Immigration Service in Denmark, where it will be processed. If the applicant is a legal resident of Denmark, the application may be submitted at the Service Centre of the Immigration Service.
If you have been invited as a researcher to teach and give lectures, you may do so without a residence and work permit, provided your stay does not exceed three consecutive month, calculated from the day of arrival in Denmark.
Citizens of a country with a visa requirement to enter Denmark must obtain a visa valid for the entire stay before arriving in Denmark.
If the applicant expects to remain in Denmark for longer than three month, a residence permit must be obtained for the entire period, including the first three month before beginning work. The permit must be obtained prior to arriving in Denmark.
Residence and work permits for researchers are normally valid for the entire period of employment indicated in the job contract.
For more information concerning residence and work permits:
http://www.nyidanmark.dk/en-us/coming_to_dk/work/researchers.htm
4. Please have a look at the checklist relevant for you: