Marugame is on the JR Yosan Line, which runs along the northern coast of Shikoku between Takamatsu and Matsuyama. Express trains from Takamatsu take 30 minutes; local trains take slightly longer. From Okayama on Honshu, limited-express trains cross the Seto-Ohashi bridge and stop at Marugame in about 40 minutes — Marugame is the first significant stop on Shikoku after the bridge.
From Matsuyama the journey is about 80 minutes by limited express. From Tokushima (on the Pacific coast), you need to go via Takamatsu, adding time. There is no direct bus connection from most major cities that is faster than the train. Marugame Station is in the centre of town and all the main sights are within walking distance.