There are actually several viable options, the cheapest would have been to buy a through ticket from the airport to Finse.
The most convenient option, but also the most expensive, is to take the Flytoget (Airport Express Train). Mo-Fr, the trains depart every ten minutes (x:00, x:10, x:20, etc), Sa+Su every twenty minutes (x:10, x:30, x:50) and take 19 or 22 minutes. They are however quite expensive with 170 NOK or about 21 Euros for a one-way ticket to the central station. You can travel without a paper ticket, which sounds quite simple, but you have to be careful not to charge yourself for a longer distance than actually travelled. Travelling from the airport is quite simple, as you must select your destination when swiping your card at the platform gate. If you travel to the airport, you must remember to swipe your card at one of the devices at the departing station, otherwise you will be charged 250 NOK (the tariff for the longest distance). There are also plenty of ticket machines where you can buy regular paper tickets and pay with cash or most credit and debit cards. If you want to pay with cash, be aware that the ticket machines won't accept larger bank notes than 200 NOK.
At least Mo-Fr, it is also a reasonable option to use the regular suburban trains instead of the express trains. They leave twice an hour (0:03 and 0:43) and take 23 minutes to the central station. These trains operate on Sa+Su as well, but not necessarily every hour. The ticket price is 90 NOK or about 11 Euros. You can buy tickets from the NSB/Ruter ticket machines or from the NSB ticket desk. If you are in a hurry, you can also buy your ticket on the train from the conductor, but in that case, have to pay an additional 40 NOK fee.
Be aware that the express and suburban trains are operated by different companies and their tickets are not interchangeable. Express train tickets are available at the orange ticket machines. Suburban train tickets are available at the red and gray ticket machines.
There are also several bus lines operating from the airport, but if you are going to the central station, the bus lines are neither a cheaper nor faster option than the suburban trains.