As an EU/EEA or Swiss citizen you may freely enter Denmark and remain for up to 3 months without registering your residence with the Danish authorities.
If you will be residing in Denmark for longer than 3 months, you need to apply for an EU residence document (also known as a registration certificate) within 3 months after entering Denmark.
If you are a job seeker, you are required to submit your application within 6 months after entering Denmark. If you are a citizen of Finland, Iceland, Norway or Sweden, you need not apply for an EU residence document since as a citizen of a Nordic country you have the right to reside in Denmark without an EU residence document. Instead you may contact the Citizen Service of the local municipality directly in order to get a civil registration number (CPR number).