By being an au pair in Norway, you can learn about Norwegian culture and language by living with a Norwegian family. At the same time, you will receive pocket money/pay for helping the family with simple jobs such as child-minding and light housework. In addition, you will have free board and lodging with your host family. You have to pay tax on the money you receive from the host family, but the course in Norwegian which the host family pays for is tax-free.
On the website of the Directorate of Immigration (UDI), you will find the rules for applying to stay in Norway as an au pair.
After you have applied for and been granted a residence permit from UDI, and had this permit registered with the police by attending a police station, you need to visit the tax office to notify them of your move to Norway. In order to report your move to Norway, you must have a residence permit for six months or more. You will then be assigned a national ID number.
When staying in Norway as an au pair and receiving pocket money from the host family, you must have a tax deduction card. You can apply for this at the same time as you give notice of your move to Norway. If you have a residence permit for less than six months, you do not give notice that you are moving to Norway, but just apply for a tax deduction card. You will then be assigned a so-called D number (instead of a national ID number).
You will normally be a member of the Norwegian National Insurance scheme from your first day as an au pair in Norway. Check with the Labour and Welfare Service (NAV) about the rules for this, and what other rights you have in the National Insurance scheme.