Moji's main station is Mojiko Station at the very tip of the Mojiko Retro district. From Kokura — the main rail hub for Kitakyushu — the JR Kagoshima Main Line runs to Moji in around 15 minutes. From Hakata (central Fukuoka) it's about an hour with one change at Kokura.
The Kanmon ferry runs every twenty minutes between Mojiko and Karato pier in Shimonoseki on Honshu — a five-minute crossing, fun in itself. There is also the Kanmon Pedestrian Tunnel for the determined walker.