The recommended mode of travel is by plane or train, and both are best connected through Stockholm airport Arlanda. There are 1-5 flights per day, round-way tickets start at €200, and the flight duration is 1h35min. There are also night trains leaving from the airport that go directly to Kiruna C without having to switch trains. They leave Arlanda at 18:35 and arrive to Kiruna at 09:14, i.e. 14h40min. Prices for one-way tickets start at €70 for a seat (not recommended) to shared sleep compartment (1-3 persons) for €100/person (or the whole compartment for €230). As always, the earlier you book, the more options you will have!
There are dedicated coaches from the airport, and also public transport.
Taxi services are limited in Kiruna and not very reliable in my experience:
There are many car rentals available from the airport and train station.
If you want inspiration for travelling to Kiruna by train, here is a video-report from someone recently taking a similar trip to nearby Luleå. It seems the first class cabins are no longer available, though.
