The statutory Norwegian-and-civics entitlement — what you get depends entirely on your residence permit.
Details
IMDi, the Directorate of Integration and Diversity, administers the rules under the Integration Act; your municipality delivers the teaching. The law splits people into those with a right and a duty to attend (free training, up to 18 months if you have upper-secondary education or above, up to 3 years if not) and those with only a duty (capped at 225 hours, and generally paid for yourself). Age and permit type decide which group you fall into, so check this page before assuming anything about cost. In practice you start by contacting your kommune's voksenopplæring office.