You can simply take a taxi from airport to town, less than $15 in my memory.
To see the northern light you need to join a local tour to go to the remote area which is about an hour from town.
Don\'t drive by yourself as it is very cold at night at -20c. They will have a cabin with warmer and hot drink/food for you to get warm. Normally the tour lasts for 3 hours as you need to wait for the light some time.
I searched it online and tripadvisor and then emailed to reserve the seats. I forgot which local agent we used. There are plenty and you can pick one with different languages and group size etc
And we paid them the first day we joined the tour.