Um there are many frameworks for dealing with REST. There are many ways to approach the problem as well.
Basically accept an HTTP request. The request could be like a regular web request, why not. The response, instead of html, would be XML, JSON, or anything that is easily understood (or you can have ".xml" for xml output, .json for json output. Ruby has lots of this behavior out-of-the-box.
The real work of REST is the serialization. I mean in one of my former jobs we converted a regular html server to serve most things as rest by replacing the view layer with something that outputs serialized objects. You can also accept input as JSON or XML or whatever by asking for a "content" paramater to contain the requested JSON.
Thats the beauty of REST, it could be very very simplistic. Just see what your users want to communicate in.
So in any case, check out Ruby on Rails' REST stuff. What language are you coding in anyways?