OK this will be longer, but there is an easy way to install Quake 3 under linux using the ioquake3 binaries. When the Quake 3 source code was released under GPL the community around ioquake3 continued fixing bugs and improving it - more details on their web http://ioquake3.org
You can get the binaries here: http://ioquake3.org/get-it
Installing using the command line (i386 system):
$ wget http://ioquake3.org/files/1.36/installer/ioquake3-1.36-7.1.i386.run
$ wget http://ioquake3.org/files/1.36/data/ioquake3-q3a-1.32-9.run
$ chmod u+x ioquake3-1.36-7.1.i386.run
$ chmod u+x ioquake3-q3a-1.32-9.run
An installer window shows where you can choose the install path (by default your home directory) and binary path (bin directory in your home).
The engine itself is released under GPL, but the textures, Quake 3 art work is still proprietary, so you will need your Quake 3 CD. Insert it in your CD-ROM (it should be mounted) and run the second installer.
You will see another window, where you can select what type of CD your have (windows/linux), then press "Begin Install" and the installer will copy all the required data.
Now just run the game by typing
$ [[your install directory]]/ioquake3
Hope this helps :)