It's much less formal than in other cultures. At the very least, we sign the legal documents and have some sort of ceremony or celebration. It's fairly common to live "de facto" (ie. officially unmarried but still as a couple), and people may use the word "partner" instead of girlfriend/boyfriend/fiancé(e)/husband/wife/spouse.
People from more traditional families would observe customs, such as "meeting the parents", "asking the father for the bride's hand in marriage", "engagement", "church wedding" and so on. I've just listed elements from the Christian tradition, but of course there are plenty of other traditions from other cultures in Australia.