We have not yet had an official release. Nonetheless, you can still get icculus.org/quake3 a few distributions or build it yourself from Subversion.
If you're lucky your distribution or someone else using it may have already done all of the work for you.
Gentoo users can just emerge quake3 to get a recent snapshot of our Subversion repository.
Ludwig "Angst" Nussel works on this project and also provides RPMs for SUSE Linux Enterprise Server. Note that these are just the binaries, no scripts or KDE/Gnome files to start them. Ludwig also mentions that the packages should work on any glibc 2.3 system.
( This part assumes Windows users are using Cygwin. If you aren't, TortoiseSVN is a good client. )
Everyone else can compile it themselves
Open code/macosx/Quake3.pbproj in XCode, press build. Enjoy!
Building on Windows is slightly complicated. You can either use Microsoft Visual C++ or MinGW. MinGW works better currently; both methods are described in the readme you already are supposed to have read.
As of now, you still need to install the old point releases before this project because they contain updated pk3 files. We mirror them for your convienience: