Your question is really broad, and not focused on Unity - no one here will be able to answer it without going through many pages of documentation and learning the http://Justin.tv API. Remember, UnityAnswers is a place for specific, technical questions about the Unity engine.

Perhaps you should investigate the http://Justin.tv API a bit more, and determine what you'll need on the Unity side. Also, take a look at the features of .NET / Mono (which is what Unity scripts run on). Then, when you have a specific question, we'll be happy to try and answer it.

To get you started, it looks like http://Justin.tv has a RESTful web interface. You can certainly access web services from Unity applications through use of the WWW class or third party plugins like UnityWeb.