According to the Department of Immigration and Border Patrol, you can visit your partner in Australia if they are an Australian citizen, permanent resident or eligible New Zealand citizen. However, to do so you must make your application under specific visa categories pertinent to your reason for the visit or your partner's visa. Consequently, here are the three major categories under which you can make your application.
Spouse or De Facto Partner Visa
If you are married to your partner or are in a de facto relationship, you can apply to visit your partner under visa subclass 309 or 820. These visa applications can only be made when you're outside Australia. They give you temporary stay in Australia, during which you can work, study and enjoy subsidized Medicare benefits. If you already have the above provisional visas, you can apply for visa subclass 100 or 801 to seek permanent stay in Australia. With a permanent visa you will be able to stay for as long as you want and apply for citizenship, if eligible.
Prospective Marriage Visa
If you have a partner in Australia, whether they are a resident, citizen or New Zealander, you can use the prospective marriage visa, subclass 300 to get to Australia. This visa is temporary and gives you nine months to stay with your partner and plan your marriage. Once married, you can apply for a permanent partner visa under the subclass 100 or 801 and thereafter seek citizenship.
Student Partner Visa
Although the above partner visas only apply if your partner is a resident, citizens or eligible New Zealand citizen, you can also seek a partner visa if your partner is studying in Australia. You can do so by seeking to be enjoined as a second applicant in their student visa application. However, this is dependent on their age and study program being undertaken. Depending on the student visa they hold, you will be allowed a set number of working hours. However, if you seek to take up a full study course, you will be required to seek your own separate student visa.
Although the main categories that a partner can use to get a visa are three, the specific visas that you have to choose from are many as highlighted above. If unsure where you lie, seek the assistance of a migration agent or immigration lawyer to understand the right visa for your needs. This is important for you to lodge the right application and get the visa the enables you visit, study, work or live in Australia.