Public Transport in Zürich (the ZVV) includes trams, busses, trains, boats and two funiculars (Seilbahnen). If you buy a ticket, you might use one or more of these to reach your destination. (Or you might just ride around and see where you go if you have a day pass and want to see more of the city.)
On Saturday we got home early from our hike and still had until 5 a.m. Sunday to ride with our passes, so we, of course, took advantage of that.
One idea was to ride one of the funiculars. In one of our earliest days in Zürich, we took the Polybahn Seilbahn which goes from the river up to the University. This 10-second video shows the little cable car in action. This video takes you on the 1 ½ minute ride.
The other funicular is longer with several stops between the bottom and the top. It is called the Seilbahn Rigiblick. (I have not found out why this part of the hill is called Rigiblick, except that it implies that you can see the mountain Rigi from there – Blick meaning view. I didn’t see that mountain, but maybe I should go back on a clearer day.)
This video gives a good idea of the steepness of the hill.