Once you’re there, Stockholm is easily covered on foot and using local buses and the metro.
Finnair flies internally including to Swedish Lapland. Otherwise, take the train from Stockholm via Lulea into Lapland — then it’s bus or snowmobile from there.
There are also daily connecting flights with SAS from Stockholm to Kiruna,
18km from the Icehotel. Trains also connect Kiruna with Lulea and
Ferries also ply the Baltic Sea, linking Sweden with Finland and the Baltic states.