On arrival in Narvik, either grab a taxi (if you have heavy luggage) or take a stroll down into the town (right out of the station, up to the main road and take a left) where you can get a taxi from the main rank in the centre to Narvik airport. It takes about 5-10 minutes (don't go to the airport at Evenes - more like 60 minutes away). It is also quite reasonable to walk to the airport if it's a nice day and you don't have to much to carry; it's about 2 km from the centre of town (so about 3 km from the station) and signposted.
At the airport you can get something to eat in the cafe while waiting for your plane to Tromsø due to depart at 1855 (this service stops also at Andennes - maybe you can spot the Rocket Range, on the coast, south of the town, or the lidars from ALOMAR, on the mountains to the south of the airport), arriving Tromsø at 2010. The 'summer price' on the plane is 410 NOK; there is no service on Saturdays.
Alternatively one can fly to Evenes (0930-1005, every day) and take the bus to Narvik to catch the train departing at 1340 (arrives Kiruna 1645).
Updated by Tony, 5 August, 1995.