About 2000 km from Moscow. The road is ok, there are plenty of gas stations and small towns where you can sleep on the way.
Siberia Airlines has several flights a week to the regional center - Murmansk. The flight takes 2.5 hours, and costs 200-250 USD (round trip, incl. all the fares). The buses are not regular, so you will need to take a taxi to Kirovsk, the ride takes 3 hours.
The closest station to Kirovsk is Apatity. Daily Train from Moscow to Murmsnsk stops there for 5 minutes. Trip takes 36 hours and costs 2000 R ($70). It will take half an hour to get from the station to the town.