In general, it’s easy to get from A to B by bus. This is a lot cheaper than to take a taxi.
The bus driver sells tickets on board, but he just takes cash (NOK). A single ticket is 50 NOK, a day ticket 110 NOK (valid for 24h). If you have the chance, you can buy tickets in advance, for example at the airport shop in the arrival hall or in the city center (the bus company’s office, Narvesen at the main square). Single tickets bought in advance are 30 NOK, a day ticket 100 NOK. Keep your ticket during the bus ride.
If you want to take a taxi, your hotel reception can call it for you. City center-University approx. 150 NOK.
Take bus 20 or 21. They run every 5 minutes in the morning, the ride takes 10min. Follow the main street towards the pedestrian part. At the beginning of the pedestrian part, you can see a lot of bus stops. Bus 20/21 stop at the upper bus stop. Get off at “UiT/ISV”, that’s the bus stop after you passed the rocketshaped planetarium on the campus.