Hi Jinny
I'm also in South Australia, but my ancestors were all English so I've had a lot of dealings with GRO. Ordering is easy, especially if you know their reference for the certificate you want (if you don't, they'll find it but then they charge more).
Start with the link Osprey gave, open an account, and look at their historical index for births and deaths. If the event you want is too recent to be listed there, or if you're looking for a marriage, try this other site which is completely free:
https://www.freebmd.org.uk/cgi/search.plFreeBMD is fairly complete up to 1983 but they don't sell certs, they just provide GRO index details.
When ordering from GRO, take the PDF option (if offered) unless you want a document to hang on the wall. PDFs are far cheaper and contain the same information without the 'official' format. They come by email in a few days, whereas paper certs take around 3 weeks by air mail.
Just ask if you'd like any more help, or you can PM me if you'd prefer
Carol