When you map a Google Site to your own domain, you first create a CNAME record in your domain registrar's control panel. Mapping must be to a subdomain. The common subdomain is "www'. So to map your site to that subdomain you create a CNAME record of type www that points to ghs.googlehosted.com. You then add your web address to your site. See
this article. Note that you can add up to 5 URLs to one Google site. If you have published the site to only a specific group of people the custom URL will redirect to the sites.google.com URL.