Arrival from Northeast
SAS and Norwegian fly from Oslo to Evenes 2-3 times per day. Several car rental companies have a branch at the airport. Their opening hours match the arrival and departure times of the major airlines.
By car simply follow the E10 to "Å i Lofoten" until Leknes and there turn left at the ESSO petrol station onto road No.815 to Stamsund. Only 6.5 km from there to your destination. About 3 hours travel time from Harstad/Narvik Airport (EVE).
Regular busses go 2 times per day from the airport to Svolvær (3,5 h), where you have to change the bus and continue to Leknes (Route 18-741, ~1.5 hrs), change bus again to Stamsund (Route 18-767, ~10 min). The closest bus stops are are either Steine Kryss (Katolisk Kloster) or Finstadveien Kryss.
Arrival from Southwest
SAS and Norwegian fly nonstop from Oslo to Bodø 5-7 times per day. Bodø is also connected to the NSB railway network, with two daily arrivals from Oslo. The fastest way to get from there to Lofoten is flying with Widerøe to Leknes or alternatively to Svolvær. The flights take around 25 minutes, with at least 6 daily departures. Car rental companies have a branch at both Leknes and Svolvær airports or downtown.
From Bodø you can also go directly to Stamsund with Hurtigruten. Departure daily 15:00, arrival 19:00 o'clock. Public busses depart towards Leknes within 15 mins after the ship's arrival. (Route 18-767, ~10 min). The bus stops closest to my house are Steine Kryss (Katolisk Kloster) and Finstadveien Kryss. Hurtigruten vessels also carry cars, but it's recommended to book in advance. Alternatively you can get a rental car from Lofoten Leiebil in Stamsund. They will even deliver it at the port upon ship's arrival, if you ask.
If you bring your own or a rental car from the mainland, you can also take the Ferry to Moskenes. Departure 2-6 times per day, about 4 hours to get to Moskenesøya. With a car during the summer season better book in advance! From Sørvagen follow the E10 to Leknes and at the ESSO-roundabout turn right and follow the road No.815 to Stamsund. Travelling time one additional hour from the ferry.
A very relaxing kind of arrival, if you are not in a hurry, is to take the Hurtigruten from Tromsø. Norway's largest town above the arctic circle is well connected to Oslo, Stockholm and even smaller cities by plane. SAS and Norwegian will get you there all year round. Lufthansa offers two nonstop flights per week from Frankfurt and Munich during winter, Edelweiss does the same from Zurich.
Hurtigruten ships leave at 01:30 o'clock and will take you over night to Lofoten. You can experience one of the most beautiful parts of the whole coastal voyage, including the Raftsund passage with the famous Trollfjord. You can even do some of their excursions, like the sea-eagle safari, while travelling to Stamsund. Arrival will be at 21:00 o'clock.