How to Access Feedly API?

Question

Google Reader dies (RIP) and finally Feedly created their own clone and also an API for external readers. This API is also open for other readers. But, how can I access this API with my own RSS-Reader? I don't see any documentation or description about it.

Answer 1

EDIT 18/September/2013:

They have a developer site now.

Original answer:

At the moment it seems access to Normandy API is restricted to a very short list of whitelisted developers. I'm also waiting to hear more about public access, because as soon as the migration happens (in two to three days) my home scripts are going to be useless.