There are even possibilities for running Windows designed games on Linux, by emulation, with a program called Wine. But I'll detail this into a future article. So, go on Ubuntu Software Center and search for OpenArena. It installs in minutes, and no additional configuration needed.
Please note that 3D accelerated graphic drivers are needed. If your computer doesn't run natively a 3D accelerated driver, go to System -> Administration -> Hardware Drivers and select the driver (if available).