Lapland may be remote, isolated, and generally far away from many places in the world...but that doesn't mean it isn't accessible. There are quite a few airports in Lapland, as well as several others elsewhere in Finland and Northern Norway that offer easy access to exploring Finnish Lapland.
Below is a map of Lapland's airports as well as a few others that many use to travel to the region. Under the map is a short listing of the airports with their designated airport code which you can use to search for flights to Lapland online, as well as a few of the nearby towns/resort areas/villages near to the airports.