How can I self-host Ubuntu One?

The Ubuntu One service is closing and being open sourced:

Additionally, we continue to believe in the Ubuntu One file services, the quality of the code, and the user experience, so will release the code as open source software to give others an opportunity to build on this code to create an open source file syncing platform.

How can I self-host the server and set up my Ubuntu One clients to use this server?

I looked at the Launchpad project site, but it seems that all the server-side code is still hidden.

You cannot self-host the server currently. It will be released as open source, meaning, some time in the future. There is still some work to do to make it possible to run it on arbitrary systems. When that happens, it should simply be a matter of using JuJu to deploy the service, or pulling it from the bzr branch and running it yourself.

Until then you will have to just wait, or write your own server based on the protocol, which is already open source.