Instructions

1. Invite a Google Apps account as owner
   

   Go to your personal Google Site and use the More Actions button and then Share this site: then add the Google Apps Account e-mail address as owner and use the Invite these people button.
   

2. Sign in to the personal Google Site with your Google Apps Account
   

   Once you have invited the Google Apps Account make sure you sign out of your personal Google Account and sign in to your personal Google Site using your Google Apps account: to do this when you get to the sign in page use the Sign in with a Google Apps Account small text link, under Sign up for Sites, under the Email and Password boxes.
   

3. Copy the Site
   

   Use the More Actions button then Manage Site and go to General: use the Copy Site link and complete the form (Site Name, URL and whether you want to keep revisions and sharing) and use the Copy Site button.

This then copies the site in its entirety to a new site in your Google Apps domain, meaning you can take advantage of the 10GB of space offered.

This also works the other way around so you can copy a site out of a domain: just invite a non-Google Apps domain user (an ordinary Google Account) as owner and then that owner can copy it out to a http://sites.google.com/sites/somewhere site.