Diaspora* is a federated open source social network. It does not have a protocol specification or an API for app support/integration. Diaspora* is not intended to be run as one server/user, but by clustering users on pods with pod administrators, etc.

Reading the API docs, it seems that every user needs their own URI to be uniquely identified. I wonder how this will work with the average user, just IP address? What about users with shared internet?

You're correct-- we anticipate users either registering their own domains (i.e. http://danielsiders.com) or using a hosted service that provides subdomains (http://danielsiders.tent.io). If you're hosting at home (dream solution here is plug computers), then dynamic DNS pointing to your home IP/computer.

PageKite (pagekite.net) is another solution for self-hosted from a household. plug

This was the mistake Open ID made, which they later realised complicated things way too much for the average user. Regular users want to identify as an email address, not a URI.

Diaspora is mentioned in the article in the "What about the federated social web?" section. Apparently it is more decentralised than Diaspora. Although I can't see what that means at the moment as implementation details are fairly sparse.

Diaspora and some other platforms are federated communities - in other words, they federate between collections of multiple people. Here, the decentralized social activity occurs between individuals. It's decentralized all the way down.