Go to your personal Google Site and use the More Actions button and then Site Permissions: then add the Google Apps Account e-mail address to the Add people box, choose Is Owner from the drop-down box and use the Share button. For more detailed instructions on how to share a site with other see the Invite people to the site section of Google Sites - Site Sharing and Visibility Options
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.
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.
If you mapped a web address to your site, e.g. www.example.co.uk, then you need to remove the web address mapping from your old, personal site and add it to your new Google Apps Site.
Go to your personal Google Site and use the More Actions button, then Manage Site and then go to Web Address. Use the Remove link next to your mapped web address, e.g. www.example.co.uk.
Go to your Google Apps Google Site and use the More Actions button button, then Manage Site and then go to General. Use the Map this site link next to Web Address Mapping and enter the web address you want your site mapped to e.g. if you want your site mapped to www.example.co.uk. then enter www. Then use the Add Mapping button to make the web address mapping point to your Google Apps Google Site.
- Make Site Public and Searchable on Google Sites - Site Sharing and Visibility Options
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.