Setting up WordPress behind Amazon Cloudfront

Many websites and places that talk about integrating Amazon Cloudfront with WordPress are simply talking about static assets. Using some caching plugin that rewrites the URLs in the page’s source to point at your Cloudfront distribution, and that’s about it. They don’t talk about how your server can be (as WP SuperCache puts it) Stephen Fry-proof. No one actually says anything about how to put YOUR ENTIRE WEBSITE behind Amazon Cloudfront (and by this, I mean pointing your www.* domain at Cloudfront and letting it take care of everything).