Basically you need a server (well, you don't NEED a server, but it would make it much simplier) that would store user IPs between other things like file hash lists, etc.
That server can be in any enviroinment you want (which is very comfortable).
Then, each client connects to the server (it should have a dns, it can be a free one, I've used no-ip.com once) and sends basic information first (such as its IP, and a file hash list), then sends something every now and then (say each 5 minutes or less) to report that it's still reachable.
When a client searchs files/users, it just asks the server.
This is a centralized network, but the file sharing would be done in p2p client-to-client connections.
The reason to do it like this is that you can't know an IP to connect to without some reference.
Just to clear this server thing up:
- Torrents use trackers.
- eMule's ED2K uses lugdunum servers.
- eMule's "true p2p" Kademlia uses known nodes (clients) (most of the time taken from servers like this).