Lofoten is without question one of the best hiking destinations in the world.
Also, Norway is very expensive.
The gateway for most people is the town of Bodø, the end of the train line north. It’s often cheaper and easier to fly as the train is a 17 hour overnight journey.
From Bodø you have options. If you don’t have your own transportation easiest is to make a loop by ferry and bus.
Take the fast passenger ferry Bodø to Svolvær. About 4 hours.
Your first hike should be Fløya & Devil’s Gate. The trailhead is about a half hour walk from the ferry landing.
From Svolvær you would take buses or hitchhike the only highway west through islands A to V to F to M.
M Moskenes (Moskenesøya) has the best hiking. Save it for last.
Reine is the best base town for Moskenes. You can do 3-4 awesome hikes out of the same town.
From the village of Å (the last letter of the Norwegian alphabet) you can catch the slow ferry back to Bodø. About 4 hours.
The weather is dreadful. For any 7 day period during the hiking season you may have several days of serious wind and rain. These should be rest days if you have time.
If you have your own vehicle — or decide to rent a car — you can go when and where you want. That’s ideal.
related – travel 2 walk – trip report: Norway – Bødo & Lofoten Islands, August 2017