Since six months I live in Melbourne and at the beginning, it took me a while to realize how the public transport system works. The Melbourne public transportation is actually pretty good and takes you not only around the city, but also quite far out to the countryside - so it’s easy to explore the city and its surroundings!
Ticket
Melbourne uses myki cards, which are plastic cards you can buy on machines or in shops. Since a little while, you can also sign up for a myki card in your Google Pay (if your phone supports NFC), so you can just charge up your card in seconds. There are two ways to pay: Either you load up myki money (= any amount of money) and pay as you go, or decide for a myki pass (starting from 7 days up to 365), if you’re using public transport regularly. With a myki pass, you only tap on once and then your pass starts running (while your pass is valid, you don’t need to touch on anymore).
Touch on and off
This was really complicated for me at the beginning, so I try to make it simple. In the city centre, you have the free tram zone. When you drive around only in the city centre, you don’t need to touch on or off as it’s free. If you plan to drive out of the free tram zone, you have to tap on when entering the tram. Almost all trams stay inside zone 1, so you don’t need to touch off. If you don’t know whether you will leave the free tram zone, listen to the announcement that comes when the tram crosses the imaginary line and in case you go further, tap on.
Buses always require you to touch on and touch off as they go longer distances. In case you go to zone 2, the fee is a bit smaller, so it’s worth to touch off. Buses don’t stop on every station so make sure you push the stop button when your stop is coming up.
Trains have big displays showing the name of each line and the next stops. If you drive around the city centre by train, you have to touch on to pass the entry points, so you will be charged. Trains are faster, but if you plan to stay within CBD and want to save money, better hop on a tram. On trains, you also touch on and off when you leave the station again.
Hope this helps you to enjoy Melbourne, have fun exploring 
