ZendCasts.com: Building a JSON Endpoint with SLIM (Part 1)
You'll need some of the base that he created in this previous screencast to follow along (the basic structure, really). His takes his basic "hello world" application and builds on it to add a "model" to pull name data from and has the "/names" action respond with a JSON-formatted message (and an "application/json" content-type). His "model" pulls the data out with findAll() and find() methods.
You can grab the source to follow along.