If you buy at a store that sell phones you will need your passport and your address (either hotel, or your home address (or any other address in your country, they won't check)), if you buy the sim at 7-eleven or any other convenience store you register your name and birthdate via sms, this process may take longer than when it's done in store.
If you arrive at OSL there is a store in arrivals (after customs) called Telering. If i remember correctly they sell both Telenor and Netcom, the two largest operators in Norway. If you're gonna use the card domestically or for data, i reccomend one of them. Telenor has the best coverage and data plans. (You pay max 10NOK per day for it)
If you're planning to call internationally i reccommend Lebara. You will find Lebara at Narvesen, also in arrivals, or many places around Norway. 7-eleven also carry them if i remember correctly. Unfortunately you will pay more for data use since they don't have any plans.
Sim cards usually cost 99NOK and has 50NOK calling time included, but this varies from store to store.
And this information is accurate. I used to work with this until two months ago.
Hope this helps