Arlanda is the main international airport in the area. It is about a 2 hr journey from Arlanda to Stjärnsund. There are trains that leave directly from the airport to Hedemora where you can be picked up or take a buss to Stjärnsund.
Trains go from all over Sweden to Hedemora where you can be picked up or take a bus the rest of the way. Trains are a great choice for eco-minded travellers.
Travel by bus can be cheaper than trains and still quite comfortable.