<p>What does RESTful Authentication mean and how does it work?  I can't find a good overview on Google.  My only understanding is that you pass the session key (remeberal) in the URL, but this could be horribly wrong.</p>

It's certainly not about "session keys" as it is generally used to refer to sessionless authentication which is performed within all of the constraints of REST.  Each request is self-describing, carrying enough information to authorize the request on its own without any server-side application state.
The easiest way to approach this is by starting with HTTP's built-in authentication mechanisms in
RFC 2617
.