UPDATE: The express boat between Narvik and Svolvær has been discontinued, as a new bridge (the Lofotens fastlandsforbindelse or "LOFAST") opened in November 2007, and allows direct car/bus access between the mainland and the Lofoten Islands. Nor-Way Bus 760 provides daily service between Narvik and Svolvær, travel time just over 4 hours. This seems to be slower than the old express boat, but oh well...
A quick way to get to the Lofoten Islands is the express boat from Narvik to Svolvær. The boat is quite small, but it goes extremely fast. It makes the trip to Svolvær in 3 hours 25 minutes. The boat also stops at Lødingen, with stops on request at Liavika, Kjeldebotn, Holandshamn, Brettesnes, and Skrova.
In Narvik, the boats depart from the ferry dock, Pier 2. Boats depart Svolvær from the main dock, on the main square between the Narvesen and the tourist office. Through 30 September 2007, boats depart Narvik Sunday-Friday at 3PM, arriving Svolvær at 6:25 PM. No boats depart Narvik on Saturday. Departures from Svolvær are at 8:30 AM on Tuesday, Wednesday, Thursday and Friday, arriving in Narvik at noon. Additional departures from Svolvær on Friday and Sunday at 7PM, arriving Narvik at 10:20 PM. No departures from Svolvær Monday or Saturday. As of June 2006, one-way fare was NOK 292, or NOK 442 for a couple traveling together.
Svolvær is a regular stop for the Coastal Steamers enroute between Bergen and Kirkenes. This is unquestionably a very scenic and romatic way to get to Svolvær. The southbound steamer from Kirkenes towards Bodø and Bergen arrives daily at 6:30PM, and departs at 7:30PM. The northbound steamer from Bergen towards Tromsø and Kirkenes arrives daily at 9PM, and departs at 10PM. Prices vary, depending on time of year and accommodations desired. You can even bring a car onboard (for extra cost, of course).
In our case, we boarded our northbound steamer and traveled for 3 nights until we reached Kirkenes. The views were magnificent! To give you an idea of cost, we got the cheapest private cabin, an "I2" cabin with no view (which I strongly recommend, by the way, since you'll be spending most of your waking hours on deck) during peak season (late June). Total cost for two was NOK 7266, plus meals.
A way to get the coastal steamer experience on the cheap is to sail from Bodø to Svolvær. Boats depart Bodø daily at 3PM, and arrive in Svolvær at 9PM. One-way passage costs NOK 398 per person for summer 2006.
You can book tickets either through the website (using the "port-to-port" option), or by emailing the company directly at "booking[at]hurtigruten[dot]com." The representatives are very friendly, have good command of English, and are tolerant (even when bone-headed customers give them the wrong credit card number by mistake... 8)
One final warning: be careful when typing in the website. If you're off by one letter, you'll be diverted to a strange "search engine," be flooded with spam, and will have a browser hijacker installed on your computer.
Svolvær's Helle Airport (Code: SVJ) is approximately 15 minutes from the town center. Widerøe offers 6 daily flights to/from Bodø, and 1 daily flight to/from Stokmarknes. If you are starting or ending your trip in Svolvær, it is possible to book your international flight all the way to Svolvær with connections in Oslo and Bodø. Also, if you're arriving by bus or train in Bodø, you'll find the plane is the quickest, albeit not cheapest, way to get to the Lofoten Islands.
The airport has a small coffee shop, but that's about it. Car rental is available from Avis and Hertz. There is no airport bus, but taxis are available.
I took ages getting the url that appears below. Sadly it's in Norwegian only but surely you can make something of timetables in a foreign language.
It's good for getting around the whole of Lofoten and beyond.