Public transport in Melbourne

Public transport in Melbourne is fairly good - we have trams, trains and buses.
The ticketing is done via the Metlink system; and you can buy these either on trams, at train stations, or from the driver when you get on the bus.
All trams (and the buses and trains up to certain stops/stations) are within Zone 1, which is the cheapest. If you want to head further out, you'll have to pay more. There is also V-line network which heads to regional areas of Victoria, and trains leave from Southern Cross Station (the main inner-city station is Flinders St Station, on the corner of Flinders + Swanston St).
The best thing to do is buy a daily ticket which allows you unlimited travel on all buses, trams and trains within the Zone you purchase it for on that date. Alternatively you can buy a 2hr ticket or a city-saver ticket (but the area this ticket covers is minimal).
If you buy a 2hr ticket after 6pm, or validate it after 6pm, it lasts till 3am, which is awesome when you're heading out at night.
Hope that helps!