@rcbconopio If you're used to SG/HK style transport then lower your expectations. It's good enough and can take you when you're in the inner suburbs/CBD but once you're outside into the suburbs that's when you need a car since buses can't reach everything.
If you're heading to Melbourne then register your myki card once you have one to protect its balance: https://www.ptv.vic.gov.au/tickets/register/
If you lose that card but it's registered, just buy a new one, top it off a bit (say $20), register new one, then do a balance transfer from your lost card to your new one ezpz.
Sydney IMO has the best public transport system out of all the AU cities. Double-decker trains and they go all the way to the west. You can get up to the Blue Mountains in 2 hours with just your Opal card.
Brisbane has the best bus network, with busways (dedicated highways exclusively for buses) running north and south of the city. It has good regional train lines but the city trains suck. You can ride a train from Central and reach the Gold Coast in 1 hour.
Gold Coast trams have surfboard stands!
Haven't used much of transport in Melbourne but I know they have a free zone around the CBD.
As for public transport:
Read up on the fare rates on using your transport card. There's peak/off-peak rates, fare zones, transfer discounts between bus/train/tram/ferries, and free/discounted weekend rates. Australian government websites are very good and informative, 99% of any question you have about a public service is on a government website somewhere.
Always tap off, or else you'll get charged the maximum fare rate
The seating priority is generally seniors/pwd/pregnant -> adults -> students. Not sure about how other cities do it but in Brisbane a student on concession fares has to stand up and give their seat to an adult
On bus stops, you must signal the driver. Just sitting there won't make the bus slow down for you.
As for which bus/train/tram to use to get somewhere, Google Maps is your friend. Google Maps is the quintessential transport app. In Sydney, Google Maps will tell you how full the next bus/train is.
Always confirm the bus/train/tram timetables. Not every train line runs up to 11pm. Some trains or bus lines will shut down over a few days for maintenance. Your state transport (PTV for Melbourne) will have a Facebook page or Twitter account where they will announce things. Follow it.
Always thank the driver and don't be a stuck up city prick 🙂