1. Enter the domain you want to buy into your web browser. If you don't see a live website, you can go to Whois.net to get the contact information for the owner. The site might also have a link you can follow that says something like 'This Domain Is For Sale.' If you click on the link, you can usually get contact information or make an offer for the domain. (reference 1)
2. Look for domains to purchase through domain name resellers if you're not exactly sure which name you want. Resellers like BuyDomains.com list domain names that are for sale. (reference 2)
3. Check out the background of the domain. To make sure the domain has a clean record and hasn't been involved in any questionable or even illegal activity, you should check it out. Many free tools are available to help with this, including services by Archive.org and AdSense Sandbox. (reference 2)
4. Make an offer to the person who's selling the domain by phone if possible. You'll get better results if you call, rather than email. (reference 2)
5. Avoid mentioning that you're trying to buy an existing domain name on forums, blogs or social networking sites. Someone else who reads your post may want to buy the same domain name. (reference 2)