How to Map This Site To Your Own Domain

Quick Method Using Godaddy

>Go to your Godaddy Account and click on My Account
>Find the domain you want to use and click LAUNCH
>Under Domain Forwarding open the dialog and Forward your domain to the subdomain  www.yourdomainexample.com and click save.
>Now launch the DNS Panel and scroll down to where you see CNAME entries
>add a new CNAME entry and add a new one for www and point it to  ghs.google.com and click save.
Now finally come back to your sites backend by clicking More>Manage Site>Web Address and enter www.yourdomainexample.com as a new address and save..

You're Done!

Other Methods (Different than Godaddy)

How do I change my site's address (URL) to my domain name (www.example.com)?

These instructions tell you how to make your Google Site appear at your own custom web address, e.g. how to make your Google Site appear at www.example.com.  Your Google Site will always appear at the sites.google.com address as you need to edit the site there and if you set your site's visibility to public viewers can access it at the sites.google.com address also.  If you map a web address to a private site Google Sites always redirects you to the sites.google.com address as it needs a secure connection to authenticate the users.

Google Sites already provide instructions on this at http://support.google.com/sites/bin/answer.py?hl=en&answer=99448, but many are unable to follow these instructions for whatever reason.  Also bcj19 has written an equally detailed step-by-step domain mapping guide on his Unofficial Google Sites Help site, which is well worth a read: it will give another perspective on the process.

You need to edit your DNS records to make this work so if your domain provider does not allow you to edit your DNS records, or add CNAME records, then you cannot follow these instructions.  If your domain provider allows you to change your nameservers then you can sign up for a free ZoneEdit account to get editable DNS records. 

You need to do different things if you're using a Personal Google Site (a site that's at http://sites.google.com/site/sitename) and a Google Site at a Google Apps domain (a site that's at http://sites.google.com/a/example.com/sitename), so I have split the answer in to two:

  1. Personal Google Site

    Before you begin you need to have access to edit your DNS records for your domain (the web address, or URL,  you want to point at your site) because you need to make or edit your DNS records.  If your domain provider does not provide you access to these then you may have to change who you host your DNS with, to another provider like ZoneEdit.

    1. Sign in to your site as owner and use the More Actions button, followed by Manage Site then go to Web Address (under Site Settings on the left).
    2. 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 by http://www.wwwizer.com/.
    3. Now you need to edit or make the required DNS record.  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.  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.google.com (some DNS providers need a trailing dot [full-stop/period] at the end of ghs.google.com.

    If you're using a Personal Google Site that's it (you may need to wait up to 48 hours for your DNS records to propegate), but if you bought your domain name through Google (and got Google Apps with it) to point it at your Google Site you need to make sure of a few things:

    1. Sign in to your Google Apps Control Panel (http://www.google.com/a/example.com) and make sure that none of the Custom URLs use the address you want.
    2. Also make sure (again in the control panel) that the domain does not have any web address mappings (under Sites and Web Address Mappings) that use the address you want (look for http://www.example.com pointing to http://sites.google.com/a/example.com/www for instance).
    3. If the address you want is in use change it to something else or delete it.  If you do delete it make sure that the www CNAME record still exists and points to ghs.google.com, as Google Apps domains bought through Google can automatically update their DNS.
  2. Google Apps Google Site

    Before you begin you need to be a Google Apps domain administrator and have access to edit your DNS records for your domain (the web address, or URL,  you want to point at your site) because you need to make or edit your DNS records.  If your domain provider does not provide you access to these then you may have to change who you host your DNS with, to another provider like ZoneEdit.

    1. Sign in to your site as owner and use the More Actions button, followed by Manage Site then go to the General tab.
    2. Use the Map this site link and then enter the sub-domain of the Google Apps domain (if your Google Apps domain is example.com then you can only point something.example.com at your site - you cannot have a different domain pointing at a Google Apps Google Site).  So if your Google Apps domain is example.com and you want to point www.example.com at your site, enter www in the Web Address box and use the Add Mapping button.
    3. Now you need to edit or make the required DNS record.  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.  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.google.com (some DNS providers need a trailing dot [full-stop/period] at the end of ghs.google.com.
      Note:
      if you purchased your Google Apps domain through Google you do not need to make any DNS changes as they happen automatically.
      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 by http://www.wwwizer.com/

    You're done, but you may need to wait up to 48 hours for your DNS records to propagate!