If the exact domain you’re after is taken, luckily, there are more domain extensions now than ever, and it’s very likely a variant of your domain will be registrable. If your ideal was a “.com.au,” try the “.com,” “.net,” or any other potential combination; if checking our domain search here, it will show you available variants when you type in a domain name. If you do manage to get your originally desired domain, you can always change your online identity with our guide here.
If you still want to get your hands on the taken domain, the next step would be a private sale. To find the right person to talk to, you’ll need to do a Whois on the domain itself; each registry has its own WHOIS lookup available, and typing in “whois .com.au” to Google, for example, will bring up the WHOIS for the .au registry. The same could be done with any other extension. You will then be able to enter the domain you want to search, which will provide some information associated with that domain. If the domain shows up with ID protection (which hides the registration details), it’s safe to assume they’re not looking for a sale; if not, you will be able to see email addresses for the registrant, who you can attempt to contact for a private sale of the domain.