There are four daily JR buses from Kobe Airport to Naruto (2 3/4 hours, ¥2950).
Naruto does have a train station, but it is pretty inconvenient for rail traffic from other major cities. Unless you are going from another city within Shikoku, but even within Shikoku, the trains are sparse at one per hour, the fastest and most direct method of reaching Naruto is to take a bus from Kansai across the Akashi-Kaikyo Bridge.
JR Bus operates daytime Awa Express buses between Kansai and Tokushima, stopping along the way at Kōsoku Naruto (高速鳴門) which is a bus stop along the Kobe-Awaji-Naruto highway. Buses run to/from JR Osaka station every 30-60 minutes throughout the day, with separate runs operating to/from Kobe once per hour (including Shin-Kobe station on the Shinkansen) and to/from Kyoto seven times daily. The one-way fare to Kōsoku Naruto is ¥3750 from Kyoto (2h 20m), ¥3150 from Osaka (2h 10m) and ¥2750 from Kobe (1h 35m). Once arriving you can connect to a city loop bus that will bring you into town (9:00-11:30, 14:00-16:30 daily), or you can walk for five minutes to the Ko-Naruto-Bashi (小鳴門橋) bus stop where you can pick up more buses. You can also walk to JR's Naruto train station in about 15 minutes.
JR's Dream Tokushima overnight bus service from Tokyo also stops at Kōsoku Naruto (9 hours, ¥9800).
From major cities located near the Shinkansen (such as Tokyo, Nagoya, Hiroshima and Fukuoka), the hassle-free way to Naruto is to take a Shinkansen train to Shin-Kobe and transfer to the Awa Express bus. Even if you have a Japan Rail Pass, the Awa Express bus from Shin-Kobe, which is not covered by the pass, is a wise investment for ¥2750. The alternative is to continue to Okayama, where you will have to change to three more trains and add an additional 1-2 hours to your journey.
Note that seats for JR's Awa Express buses can be reserved at Midori-no-Madoguchi locations at major JR train stations.
Naruto is the starting and ending point of the 88 Temple Pilgrimage course around the entire island of Shikoku, which is traditionally covered with a person's own two feet.
Naruto claims to be home to the world's best sweet potatoes (kintoki), from which all sorts of products are derived: cakes, cookies, and liquor (Naruto Kintoki Shochu).