To apply for a com.au, net.au, org.au, asn.au, or id.au domain name, choose your preferred registrar and follow their application process. Some registrars provide services directly to the public, others may use resellers.
See the list of auDA accredited registrars.
To apply for a gov.au domain name, follow the process at http://www.domainname.gov.au/.
To apply for an edu.au domain name, follow the process at http://www.domainname.edu.au/.