You can set up a sole proprietorships (enkeltpersonsforetak), a private limited company (aksjeselskap), a general partnership (ansvarlig selskap) or a foundation (stiftelse). All business should be registered in a Coordinating register (enhetsregister). The Brønnøysund Register Centre is a place to start.
More information
All business must to be registered in a Coordinating register (enhetsregister). The Brønnøysund Register Centre is a place to start, see: https://www.brreg.no/home/.
The registration may be done electronically.
You need to have some initial capital to start and there will also be a small fee for the registration process.
Innovation Norway offer a list of services, including financial support for start ups: https://www.innovasjonnorge.no/en/start-page/our-services/start-ups/