The physical data connection to the board is RS-232-C running at 9600 baud (8-N-1) with RTS/CTS flow control. There's a couple of options from here to get to the Internet. The classical method is via a serial line protocol like SLIP or PPP to a dialup modem. This requires a TCP/IP stack on the machine to handle the rest of the layer-2 and layer-3 network protocol. This would involve porting a stack like uIP and is still some way off in terms of development.
An easier way to connect is via an IoT Wifi/Ethernet-to-UART module. Shown below is the Novasaur with one of these modules to support an Ethernet network connection (also shown with HDMI).
These modules are a bit of a cheat though. They not only adapt the physical Wifi/Ethernet interface but also contain a micro-controller to handle the TCP/IP connections. The payload is pulled out of the protocol and then sent over the RS-232 like a simple UART serial connection.
In fact, the current serial terminal program can already display protocols such as HTTP. The (blurry) image below shows a browser connecting to the Novasaur and asking for a web page. The HTTP protocol is just echoed to the screen, but a client program could interpret this and serve up a web page in response.
A web server is also some way off. The good news is the 8080 CPU is partially tested and running. There's still a lot more to test and plenty of bugs to chase down over the next few weeks. After that a simple monitor program can be added and the work to bring up CP/M can begin.