From [wiki=103a821a3a6a0b923c9f74a39662bb51]Zürich[/wiki] Hbf an hourly S-Bahn suburban train, line S16, runs towards Thayngen, stopping at [wiki=50c63b22cf2b15c4da2bb678943ba400]Winterthur[/wiki] among others and taking 57 minutes to Schaffhausen. A single ticket costs CHF 26.60/adult or CHF 13.30/child; however, if you have an all-zone Zürich day/monthly/annual pass, this is reduced to CHF 8/adult or CHF 4/child. For visitors to the Rheinfall, which is south of Schaffhausen, an all-zone ZVV pass is sufficient, see below
From [wiki=2b29c5739ec4158573c66d2124e2c7e9]Zurich[/wiki]: Take the A4/E41 direction north. It will lead you right into the city. Note that you need a vignette for all Swiss motorways.