I have no idea what the canonical answer (or answers) might be, but if I were designing it, it would look pretty much like email does now -- a store-and-forward network. You'd send your email, appropriately addressed, a DNS-like system would determine the required destination world, and the next available xboat (or other mail transport) headed in that general direction would have your message uploaded to onboard storage. Repeat routing and transloading until it arrives at the right world, at which point a planetary internet takes care of the final delivery steps.
The biggest wrinkle compared to our current internet is that the high latency makes it matter a lot how far away your recipient is. Within a few light-seconds -- say, between Earth and Luna -- you can just put up with latency on requests to servers on the other side of the zone. Beyond that, you really need to think about moving the data closer to the recipient.
Actually, it ends up looking like a cross between email and a CDN. :)