Companies such as Moneybookers and Neteller have been very popular in Australia for several years now. Being able to make simple transfers of money into and out of a bank account is the easiest and safest route that helps keep budget minded players on track.
One of the most popular methods that Australians are using is Poli (the equal to Paypal in America) where a small registration to use the service will allow funds to be transfered from the users bank into an online casino, or even online services that also allow Poli to be used.
Of course with every payment method comes the question of what money is paid into the casino itself. If Australian dollars are used for an online site offering that specific currency, then it won't be a problem. Most online casinos will offer specifics for their online prices for playing.
It's not uncommon for some sites to advertise their offers in the currency that is most common in the gambling industry. USD or GBP is the most commonly seen, though it wouldn't be uncommon to see the currency in your own country being advertised in an online casino. Gamers should be aware to budget ahead for currency conversion when playing for different currency amounts.