Every state has their own transport companies and therefore there are different ways to get around. Of course in most cities you can still buy paper tickets or pay with cash on public transport. In most cases, it will be cheaper to buy a 'transport card' to use while travelling locally.
If you are looking for ways of transport to get from one place (state) to the other (state), or if you are looking for a hop on hop off bus or a great train trip or you want to rent a campervan/car, please contact the staff of the Australian Backpackers Work and Travel Programs and they will help you out.
New South Wales
If you travel a lot in New South Wales, the best option is to buy an Opal Card.
This is a card on which you can put money and use it for buses, trains, light rails and ferries.
You can buy an Opal card in various shops (newsagencies and convenience stores) and at the stations.
Opal cards you can use for travel on public transport in Sydney, the Blue Mountains, Central Coast, the Hunter and the Illawarra. Just add value on your card before you travel and tap on and off.
You can still by single trip tickets if you wish on most services, however prices are more expensive than using an Opal car.
No matter how much you travel with an Opal card you never pay more than your Daily, Weekly or Sunday Travel Caps.
Sunday $2.60 (yes...just $2.60 for all Sunday, even the ferries and trains)
When you have paid for 8 trips in one week (counting from Monday to Sunday), you will only pay half price for the rest of the trips you do that week.
When you want to go to the airport you can also use your Opal card. Please note you will pay an additional station access fee on top of your fare (which is $14.30).
For all info on transport in NSW: http://www.transportnsw.info/
How much will it approximately cost you?
If you travel a lot in Victoria, the best option is to buy a MYKI card (similar to the Opal card in NSW).
This is a card on which you can put money and use it for travelling on Melbourne's trains, trams and buses, V/Line commuter train services and buses in Seymour, Ballarat, Bendigo, Geelong, the Latrobe Valley and Warragul.
For all info on transport in VIC: http://ptv.vic.gov.au/
In Melbourne there is a Free Tram Zone, where you do not have to pay for any public transport. Keep this in mind before you buy a Myki card that you might not need. If you start or finish your journey outside the Free Tram Zone your journey is not free.
South East Queensland
If you travel a lot in South Queensland, the best option is to buy a go card.
You can use this on all TransLink bus, train (including Airtrain), ferry and tram services in South East Queensland (Brisbane, Ipswich, Sunshine Coast and Gold Coast regions).
TransLink also operates in Cairns, Mackay, Toowoomba as well.
Regional you have qconnect (bus services).
For all info on transport in QLD: https://translink.com.au/tickets-and-fares/go-card
Check TransLink (also operates in Brisbane) - https://translink.com.au/cairns.
For in the Cairns suburbs, the public transport service, Sunbus, operates throughout Cairns; from the northern beaches to the southern suburbs via the CBD.
Private bus lines operate services covering Port Douglas, Mossman, Kuranda, the Atherton Tablelands and Mission Beach.
For all info on transport in QLD: http://www.sunbus.com.au /
If you travel a lot in Adelaide - South Australia, the best option is to buy a metrocard.
You can use this card on the bus, train or tram.
For all info on transport in SA: https://www.adelaidemetro.com.au/
If you travel a lot in Perth - Western Australia, the best option is to buy a SmartRider.
For all info on transport in WA: http://www.transperth.wa.gov.au/
When travelling a lot in Darwin or Alice Springs, you might want to consider buying a Tap and Ride card.
For all info on transport in NT: https://transport.nt.gov.au/