1. Sign in to Google Webmaster Tools with the site owner account
  2. https://www.google.com/webmasters/tools/home?hl=en
  3. Use the red Add a site button and enter the domain (not your sites.google.com URL) you want to map to your site, so if you want to map www.example.com to your site add example.com and use the blue Continue button.
  4. Go to the Alternate methods tab, choose the Domain name provider option and choose you domain name provider from the drop down list: if the drop-down list does not contain your domain name provider choose Other.  Follow the instructions Google provide to add the TXT verification record to your DNS.  If you cannot add a TXT record to your DNS Google Webmaster Tools also offers verification by a special CNAME record.
  5. While you edit your DNS you need to add the DNS record to point the web address to your Google Site. If you own the domain example.com and want to make your Google Site work at www.example.com then you need to make a CNAME record of www that points to ghs.googlehosted.com (some DNS providers need a trailing dot [full-stop/period] at the end of ghs.googlehosted.com. )  Since all DNS providers let you edit the records differently it is impossible to give precise instructions for each DNS provider, but this is what you need to do in all cases.
  6. Sign in to your site as owner and use the More button, followed by Manage Site then go to Web Address (under Site Settings on the left).
  7. In the box under Add a web address enter the address you want to point at the site, www.example.com for instance.
    Note: you cannot point a naked domain to a Google Site (example.com - no www) as this is not something Google Sites supports, but if your domain provider allows you to redirect/forward the naked domain (e.g. GoDaddy, eNom and ZoneEdit do) then redirect/forward the naked domain to the www address.  If your domain provider does not support naked domain redirection or forwarding  then just make an A record of @ and point it to 174.129.25.170 as this is a free redirection service offered


Links

http://www.steegle.com/websites/google-sites-howtos/googlesites-frequentlyaskedquestionsfaq#TOC-How-do-I-change-my-site-s-address-URL-to-my-domain-name-www.example.com-


https://support.google.com/sites/answer/99448?hl=en-GB


http://en.wikipedia.org/wiki/CNAME_record