Depending on your purpose for entering Australia, there are a variety of visa options that dictate what activities you may engage in and how long you will be allowed to stay. The specific visa you need to obtain before coming to Melbourne will depend upon these factors. Those wishing to temporarily travel the country or find casual work will need a different visa than those looking to stay long term or permanently.
The Australian Department of Immigration and Citizenship categorize visas by class type, and grant them based on a number of factors such as relationship to Australian citizens or sponsorship by an Australian business. Those looking to relocate for career reasons may be assessed based on their skills and the level of demand for those skills within Australia.
All long term visas require the applicant to supply thorough evidence of good health and character, and supporting documents to prove claimed relationships.
Visitors to Australia of all nationalities must obtain a visa before travelling to Australia (with the exception of New Zealand citizens travelling on a New Zealand passport, who are granted electronic visas upon arrival).
It’s also worth noting that the Australian Department of Immigration and Citizenship hold comparatively progressive policies concerning same sex couples. In regards to visa applications, same sex partners are assessed the same as heterosexual de facto couples; both as partners and as parents.