Clean Install Of Ubuntu Server over the network?

PXE booting

What you are looking for is called PXE booting. It means you have 1 computer (the PXE server) running on your network, which will install ubuntu on other computers on the network. When a computer on the network is started, the PXE server kicks in and starts an ubuntu install.

The setup process is pretty complex and only really usefull if you have to manage a lot of systems. A complete manual can be found on these Ubuntu help pages.

Unattended installation

Another possibility is creating an unattended CD. Also help pages provided by Ubuntu for this. Note that it does require a keyboard and screen on the new installed computer, but you might manage to do this without a screen (by hitting enter when you think the PC is ready :p). You basically create a new ubuntu CD, which will read an installation configuration file you provided.