If you are an expatriate, access to public health facilities and medical treatment depends on how long you plan to stay in Norway, on your status in the country and where you come from.
Generally speaking, the minimum length of time you need to stay in Norway to be eligible for registering with the Norwegian National Health Scheme is 12 months. If you fall into this category, you will receive the same medical assistance as Norwegian citizens.
Health insurance for European citizens
Danish, Swedish, Finnish and UK citizens receive urgent medical treatments in Norway for free.
EU/EEA citizens, Icelanders or anyone from Switzerland who is in possession of an EHIC-European Health Insurance Card are allowed to access the health care services if they're staying in Norway for a short period of time. Remember that this card is issued for free by local authorities in every EU member state. Every person insured or covered by the Social Security System of one of the states above mentioned can apply for this card.
Note that the card doesn't cover treatments for illnesses you had before you left your country. This was done in order to prevent European citizens from travelling abroad to get better treatments.
Bear in mind, for students and post workers who plan to stay in Norway for a relatively long time the range of available treatments may be more extensive than for a tourist that stays for few days.
Health insurance for Non-EU citizens
If you come from a country outside of Europe and are planning to stay in Norway for less than three months you probably need to get private health insurance.
Non EU citizens who are planning a 3-12-month stay in Norway can apply for their membership in the Norwegian National Health Scheme. The application form must be handed to the local social security office.
Note that membership in the Norwegian social security system is granted depending on whether the applicant's country has an agreement with Norway. In some cases, the range of treatments covered might be restricted for expatriates.