If you work legally in Denmark, you are covered by the Danish health insurance system. Most examinations and treatments are free, but you need to register and get a health insurance card.
On arrival to Denmark and registration at the national register (CPR) you are able to choose a general practitioner (GP) at the same time.
The general practitioner (GP) is your access to the public health care system. The GP can treat some problems instantly, and refer you to more specialized examination and treatment by a specialist or hospital if necessary.
No referral is required if you are in acute pain and need help immediately. Here you can go to the emergency ward. Dentist are private practitioners and do not require referral from the general practitioner.
The general practitioner and hospitals are free of charge.