Zermatt is a no car village. There are only electric vehicals which run around this place.
Must visit in your Switzerland Trip. locations to many Bollywood movies like Bachna ae haseeno.
It lies at the upper end of Mattertal at an elevation of 1,620 m (5,310 ft), at the foot of Switzerland's highest peaks. It lies about 10 km (6.2 mi) from the over 3,292 m (10,801 ft) high Theodul Pass bordering Italy. Zermatt is the southernmost commune of the German Sprachraum.
Swiss Travel Pass only includes the train ride till the Zermatt station, if you want to use the Mattherhorn Glacier expres you need to reserve a seat in that train at an additional cost.
The trip cost will be available right outside the Zermatt station in the place I have mentioned in the video.
Zürich is definitely easiest. You can get a train direct from the Zurich hb to Visp and change there to go to Zermatt. It takes about 3.5 hours.