Say, you want to change your website's domain from
example.com. It is a 2-step process: first clone your website on the new domain, then remove the old website.
Go to the Templates page and find the link at the bottom: Clone Boomla website by its domain. (Hit Ctrl+F and use your browser's search if you can't find it, it's there just de-emphasized.)
Enter the website's domain that you want to clone, in our case
On the next page, enter the new website domain you want to use, in our case
You may want to point your domain to the Boomla infrastructure if you haven't already.
Once your new site works, delete the old website