By train you go to Schwyz, train station and change there to bus line no. 1 direction Muotathal. Get off at the Illgau cable car stop and take the Ried - Illgau cable car, which will take you to the village of Illgau, where you walk about 200 metres eastwards to the valley station of the Illgau - St. Karl cable car.
Timetable SBB
Timetable AAGS