I feel like all of the people who just say "they're an island" are kind of diminishing the accomplishment, so I'd just like to point out a few things:
One, we had 9mil visitors in 2018, so it's not an island nobody ever visited in the here-be-dragons section of the map.
Two, we still have 3K people flying into Sydney per week, so it's not a completely isolated place. We're even allowing visitors from NZ without requiring quarantine.
Three, we have higher urbanization than the US or UK, so most of the population is living in a few cities. We're not all spread out 5 miles away from each other. So it's a comparable problem to that faced by other countries in that regard.
Four, even as an island, Covid still got here. So it could still spread once here. but we never lost control of the spread(Semantics, I know, you could argue that Melbourne lost control and that's why there was a lockdown). That's due to the steps taken to prevent the spread, but this _never really gets discussed_.
Five, and this is the important thing I think everybody overlooks, NSW has had cases in the community, but we've NOT had exponential growth and a lockdown. We're handling the problem in NSW without lockdowns, which is what a lot of anti-lockdown protesters think should be done. But every time Australia is mentioned, nobody discusses how this is accomplished, how it could be better, what others could learn from it. No, it's only ever "Hurr, Durr, They're an Island".
So, to actually discuss how Australia does it...
I personally think that the contact tracing in NSW is second to none. They take a lot of steps to be able to contact everyone who comes in contact with a positive case as quickly as possible, and this means that each positive can only really infect one or two people before they're isolating. A lot of people are told to isolate because they came in contact, then they never pass on the covid.
They also test waste water so they know if there's undetected covid in a region, like Bathurst, then ask people in that region to get tested. It's better than "wait until cases come forward".