Generally, you will need to either be married to your partner or, at the least, be able to show that you and your partner have lived together in a de facto relationship for at least 12 months before applying for the Onshore Partner Visa (subclass 820 and 801) (with some exceptions).
The application is undertaken in two stages: first, the subclass 820 temporary Partner visa, following which you can be considered for Australian permanent residency through the subclass 801 permanent Partner Visa (usually two years after the application was initially lodged). The Partner (subclass 820/801) Visa is also comprised of two main components: the main application, and the sponsorship application (undertaken by your partner).