Arriving in Shikoku is easy enough. Just land at any one of the four major airports in Shikoku: Takamatsu, Matsuyama, Tokushima, and Kochi. But then, how should you get around?
You could rent a car and that would be okay. I like to drive, but also I like to ride around in a slow enough moving train too. From the seat of a train you can look out the windows and really see much of the beautiful Shikoku countryside as you cirlce the whole region. Trains are easy to use, very very very clean, JR Shikoku staff are kind and classy, and you can really get a unique insight into Japanese local color and culture.
Japan Rail Shikoku has served this region for decades. Check out their English website and plan your trip to see all four regions of Shikoku. There is so much to see and take in, and you deserve to take your time seeing it.