As you already know, your URL has two possible formats:
www.yourdomain.com and yourdomain.com.
When using Google Sites for your website, setting up the “www” version of your domain is easy and is detailed in the Google Apps setup instructions. However, Google Sites makes it clear that at the current time you cannot — via Google Apps – get the “non-www” version (or naked version) of your domain to link to your Google Sites website.
So here’s how to setup a simple domain forward in GoDaddy for the naked domain:
1. Login to GoDaddy and head to your account management section.
2. Select the domain in question and then next to the “Forwarding: Off” option, select “Manage”.
3. A popup window will appear. In the window, enter the url TO which you wish the naked domain to go to (sorry for the “TO”‘s here):
So you would enter “www.mydomain.com” (without the quotes). Note you can also click the “Preview” button at the top right to make sure the forward is going where you expect.