Fly; but that is not easy either. You need to be there for a purpose; it is not an individual tourist destination but a research station and they (locals, authorities) don't want tourists hovering about. Unless you are visiting someone up there - that changes things somewhat. The best option to visit is to join one of the regular cruises that stop by. These start from Longyearbyen and drop by Ny Ålesund and Magdalenafjorden on the way to the northern tip of Svalbard. But the cheapest will still be flying. Check with transport authorities in Longyearbyen, it's all organised from there, not from the mainland. I may have some references on my pages, can't really remember.
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