The following samples and tutorials show you how to use API.AI:
My Buddy - A very simple "hello world" type sample that asks a question to ascertain if you can be buddies with the action's persona. This sample gets you started with API.AI and has no dependencies on webhook fulfillment.
Google Facts - A simple action that shows how to do webhook fulfillment and how to use contexts.
Guess a Number - A complex action with an involved dialog that shows how to use all of the major API.AI features.