For a very thourough introduction about GRASS (and Linux) installation, please see A.P. Pradeepkumar's Absolute beginner's Guide to GRASS Installation (PDF, 277K).
Binary packages have been created for major GNU/Linux distributions . The can be downloaded at GRASS downlaod page
In Mandrake 9.0 and later, GRASS is included in the contribs. To install use the Software Installer in the Mandrake Control Center, or run 'urpmi grass' as root.
GRASS is included in Debian testing and unstable. You may also check Debian GIS repository
SuSE rpms are avalaible on GRASS download page.
You can buy the FreeGIS CD which contains GRASS and much more.
You can also download and compile the entire source code yourself. This allows you to have access to the code and modify it if you would like to.
The source is more or less platform independent and is available at http://grass.itc.it/download/index.php. For GRASS 6.0 get the grass-6.0.0.tar.gz file, put it into the directory of your choice and decompress it with:
gunzip grass6.0.0.tar.gz; tar -xvf grass6.0.0.tar
tar -xvzf grass6.0.0.tar.gz
Then follow the installation instructions also included in the source code archive you downloaded. Also, don't forget to read the list of required software or the chapter called Hardware and software requirements in this tutorial.