Update 2: It has come to my attention, while trying to play UT3 myself after many years, that the GameSpy aspects of the game no longer function due to the incompetence of IGN and the concept of DRM’d games. There’s a pretty good chance that nothing about setting up a UT3 Server, other than for LAN play, will work anymore since the GameSpy servers have been taken offline. This means no logging into the GameSpy account for you or your server, so no online authentication, leaving only offline play.
Update 1: I have updated the links that were broken, and some formatting & informational changes.
Surprisingly there are no complete blog postings or forum topics that tell you how to set up a UT3 Internet Server from start to finish…so here we go (this guide will primarily focus on a Windows install, but I will include as much info as I can for Linux):