Unlike countries like the United States where consumer-facing sperm banks let you browse hundreds of donor profiles online and have a vial shipped to your door, Australian clinics run their own donor programmes.
You can't buy donor sperm. It is a criminal offence to give or receive ″valuable consideration″ for human tissue, including sperm.
What you'll actually do: register with a fertility clinic, join the donor waitlist, receive limited non-identifying information about an offered donor (medical history, physical description, sometimes a short personal statement), and decide whether to proceed with treatment. Treatment usually happens at the clinic via IUI, though some AU clinics might release sperm for home insemination in certain circumstances.
A note on terminology: we called this page ″Using a clinic donor″ because that's what the AU model actually is. You'll still hear people search for and refer to ″sperm banks″, which is the same thing in conversation, just different model in Australian reality.