By ship
Shimonoseki Port (http://www.shimonoseki-po...) 1-1 Nabe-cho is a short walk from JR Shimonoseki Station. There are high-speed ferries throughout the day from Moji Port in Kitakyushu.
Daily ferries run by Kampu Ferry (http://www.kampuferry.co.jp/) tel. +81 083-224-3000 connect to Busan in South Korea. Ferries leave Busan at 8PM and arrive in Shimonoseki at 8AM the next morning, and leave Shimonoseki at 7PM for an 8:30AM arrival in Busan 8AM on Monday. 2nd class one-way tickets cost ¥9000, making this the cheapest way to get from Japan to another country. Arrive a few hours early for visa inspection, though!
There are also twice-weekly ferries to and from Qingdao, China on Orient Ferries (http://www.orientferry.co.jp/) leaves Qingdao M,Th; arrives W,Sa and one from Suzhou, China on Shanghai Shimonoseki Ferry (http://www.ssferry.co.jp/) leaves Suzho Tu, arrives Th. A 2nd class one-way ticket costs ¥15,000.
By bus
The Dream Fukufuku bus runs overnight from Tokyo and Yokohama 15 1/2 hours, ¥13000. Another Fukufuku departs nightly from Osaka Umeda 10 hours, ¥9150.
By car
For those travelling the expressways and only wanting a bit of fugu, even the Nexco Parking Areas either side of the Kanmon Bridge offer it in a variety of pre-prepared forms including frozen sashimi omiyage platters. The views are rather nice too making it a worthwhile break regardless.
For those travelling by way of thumb, note the aforementioned parking areas are easily accessible on foot and frequented almost as much as the standard Service Area. The Kyushu side stop services northbound traffic and the Honshu southbound.
By train
JR Shimonoseki Station is the next-to-last stop on the San'yo Main Line and the last stop on the San'in Main Line. Shin-Shimonoseki, the Shinkansen station, is about seven minutes away by local trains and buses. However, only the all-stops Kodama trains stop at Shin-Shimonoseki, along with three daily Hikari trains in each direction toward Hakata in the morning, from Hakata in the evening.
If you're coming from a long distance, the best option is to take a Nozomi or Hikari train to Kokura on Kyushu, and then backtrack on the San'yo Main Line via Moji Station in Kitakyushu. By this route, Shimonoseki can be reached by Nozomi in about 5 1/2 hours from Tokyo and 2 1/2 hours from Osaka.