Prerequisites: The domain have to be verified in google
create and publish a site in google sites
note down the url for the site, this case was sites.google.com/itsense.no/test
go to your admin panel and search for Custom URL or use link https://admin.google.com/ac/apps/sites/address
Add a custom URL
Site type: New Sites
Google Sites URL is your published url. In this case sites.google.com/itsense.no/test as noted above
remove https:// and /home when adding the address
The custom URL for your verified domain - in this case test.itsense.no
you will get the instructions on what to add to your dns
log in to your domain provider and add the following CNAME
Add a CNAME record pointing to google sites
Type CNAME
your site url - this site uses test.itsense.no - you need to use your own site
CNAME data - ghs.googlehosted.com
After making these changes, it may take several hours for google and DNS to update