The Google Wave website communicates with the Google backend servers using an asynchronous message system based on Json.
There are roughly two phases identified in the communication protocol:
The handshake establishes a connection between the Google Wave server and the Google Wave website. This process is decribed in more detail in the Handshake page.
When the handshake has been established, the Google Wave servers and the Google Wave website communicate messages between eachother. This process is described in more detail in the RPC communication page.