Serving the city is Skellefteå Airport , which is a hub for charter flights in Norrland. Regular services are avalible daily to Stockholm-Arlanda by SAS and, a bit surprisingly, to Girona (low cost airport near Barcelona) by RyanAir.
Arriving by train is not possible, in fact Skellefteå is the largest city in Sweden without passenger traffic. Most convenient is to hop on night trains to either Umeå or the small town of Jörn where connecting buses will take you to city center.
Long-distance buses is a cheap alternative and runs daily towards Stockholm or further north in Norrland.