How to build a RESTful API?

Question

The issue is this: I have a web application that runs on a PHP server. I'd like to build a REST api for it.
I did some research and I figured out that REST api uses HTTP methods (GET, POST...) for certain URI's with an authentication key (not necessarily) and the information is presented back as a HTTP response with the info as XML or JSON (I'd rather JSON).

My question is:

1. How do I, as the developer of the app, build those URI's? Do I need to write a PHP code at that URI?
2. How do I build the JSON objects to return as a response?

Answer 1

Another framework which has not been mentioned so far is Laravel. It's great for building PHP apps in general but thanks to the great router it's really comfortable and simple to build rich APIs. It might not be that slim as Slim or Sliex but it gives you a solid structure.

See Aaron Kuzemchak - Simple API Development With Laravel on YouTube and

Laravel 4: A Start at a RESTful API on NetTuts+