Public Transportations in South Australia or anywhere in Australia are accessible.
And there are range of transportations that you may use including:

Buses plenty of buses around Adelaide and surrounding towns
Trams runs from Glenelg to Adelaide City; free tram ride starting from South Terrace tram station
until Adelaide Entertainment Centre or Adelaide Botanic Gardens
Trains runs from North to South, East to Western parts of Adelaide
Uber download an app and there are plenty of uber running including countryside
Didi download an app
Taxi just call them to pick you up

If you want to travel Adelaide using buses, trams or trains, I recommend you to buy Adelaide Metro Card because the fare is cheaper than the ticket. For example if you buy 1 ticket (single trip ) is
$ 3.80, if you use your metro card, you will only pay $1.80 during not peak times 9:01am 2:59 pm.

To know more about Adelaide metro, please visit their website:
https://adelaidemetro.com.au/Tickets...
so you will be informed about what type of card you should buy, where to buy metro tickets or cards and the fares.