Tihany is easiest from Balatonfüred, which has regular train and bus connections from Budapest. From Balatonfüred, local buses run to Tihany village and the ferry area, though frequencies vary sharply by season.
From the south shore, use the ferry between Szántód and Tihanyrév. It is one of the most scenic shortcuts on Lake Balaton and saves a long detour around the western end of the lake.