Linking Google site to a custom domain

As this process was a bit messed up in the past, here are the steps that currently work when mapping a site on Google Sites to a custom domain:

1. Create a site on Google Sites
2. Go to Google Webmaster Tools, Add a Site, type the custom domain name. This will provide instructions on registering the domain. Option of adding a TXT record is quite simple so I'll use that.
3. Go to your domain provider control panel. Add a TXT record for the custom domain. For the value, use the code generated above.
4. Back to Google Sites, go to Settings -> Manage Site -> Web Address. Type in the custom (full) address into the input box and click Add button at the top of the page.

That's it. The domain should be recognized immediately.
The instructions from Google are here.