If you are using the stand-alone version of Google Sites, the content that follows does not pertain to you. Feel free to skip this step and move on to the How do I Map My Site to My Custom Domain? article.
For Google Apps users, there is often confusion over whether they have mapped the Google Sites service for their domain or a specific Site from their domain to their custom URL. (This is not an issue with stand-alone users.) To clear up this confusion, it may be easiest to recommend that you always map specific Sites from the General tab under More Actions >> Manage Site while editing the given Site. Of course, this is avoiding the issue, so I'll at least point out the different options available to Google Apps domain administrators.
First, on the Sites Settings >> General tab of your Google Apps control panel, you will see a "Web Address" section with a link to "Change URL". Clicking this link brings you to a "Change URL for Sites" page that gives you the option to either use the default Sites service URL for your domain or to create a custom URL. Changing this value - and creating the associated CNAME - changes the URL for the Sites service, not a specific Site.
Also on the Sites Settings screen, you will find a second tab named "Web Address Mapping". This is where you need to go to map a specific Site to your custom domain. (I will cover the process for mapping a Site to your domain later in this post.)