If you want to use public transport, you have to buy a ticket; tickets can be purchased at machines in a tram, from the driver in a bus, or via the app.

GrazMobil App
The official app of the public transport provider in Graz offers a route finder, station maps and timetables, and allows for easy ticket purchases (Goole Maps does not work with public transport in Graz).

You can download it here for Android and iOS.