To buy a domain on HostGator, log in to your account and click on Domains. On the Domains page, click on the Add a domain link in the top left corner. Enter the domain name into the Add a domain form, and click on the Buy now button. You will be asked to provide some basic information about the domain, such as the name, contact information, and the purchase price.
Once you have completed the form, HostGator will check the availability of the domain name and contact you to confirm the purchase. If everything is in order, HostGator will transfer the ownership of the domain to your account.