By car
The inter-island expressway will get you from Akashi to Naruto, but it isn't advised unless you're willing to part with ¥5000 in tolls. Furthermore, signage is in Japanese and may be incomprehensible to a foreigner.
By bus
A more affordable option than private cars are highway buses, which charge around ¥600 for crossing the bridge and ¥1800 for a one-way trip from Kobe to Sumoto.
By ship
Even cheaper and more scenic, but available for the northern crossing only, are ferries that cross from Akashi to Iwaya for a mere ¥320 on the slow boat all of 24 minutes (http://www.taco-ferry.com...) or ¥450 for the fast boat a zippy 13 minutes via the Jenova Line (http://www.jenova-line.co...) located south of JR Akashi Station.
By plane
Highway buses connect Kobe Airport and Sumoto four times daily two hours, ¥2000.
A highspeed ferry used to run between Sumoto and Kansai International Airport but this service stopped in 2007.
By train
There are no direct train services to Awaji Island. Highway buses run directly from major train stations, such as Shin-Kobe on the shinkansen ¥1800 to Sumoto, and Osaka and Sannomiya stations on the regular JR line ¥2300 and ¥1800 to Sumoto, respectively. From Shin-Osaka station you must either take a local train one stop to Osaka station, or remain on the shinkansen to Shin-Kobe, to transfer to the bus.
Buses to Awaji Island are not valid with the Japan Rail Pass. Tickets can be purchased from "Midori-no-Madoguchi" locations at each station.