The api is basically a clone of Google Reader's unofficial API. As much as we hate to blindly copy it, we have to so we can be compatible with current clients. The API is pretty much documented on the above link, but not everything will be implemented here. I will document only the implemented part with some notes where applicable.
If you are an App developer and have current integration with Google Reader, all you have to do is change www.google.com to www.inoreader.com and your app should work straight away. Please write to me (jacketbgbgATgmail.com) if you have any issues with integration.