The closest train station is Kiruna, which is connected to northern Norway via Narvik, and Swedish Lapland destinations Abisko, Luleå, Jokkmokk and Gällivare (Inlandsbanan). Book your tickets with SJ. You can book transfer from Kiruna train station with Icehotel.
If you’re staying in Kiruna, you can travel to Jukkasjärvi with local bus 501. Note there are very few departures daily and periods of the year when some departures don’t run, so check the timetable before your trip. Tickets are purchased on board by credit card or at the bus station in Kiruna. Timetable
Taxi rates from Kiruna Airport are approximately SEK 400 and from Kiruna to Jukkasjärvi SEK 450 (prices may vary depending on taxi company). Local cab companies