MySQL can be downloaded from http://www.mysql.com/or mirror sites worldwide. It is also available in packaged binary format for various operating system distributions, including RedHat and Debian linux.
Installation instructions come with the software, but in brief:
Download the appropriate RPM packages, and type rpm -i packagename.rpm
Use apt-get, dselect, or dpkg to install the .deb packages. For instance, apt-get install mysql.
Download the tar.gz file from http://www.mysql.com/ and read the README file. Then type ./configure, make, and make install.
Binaries are available for many platforms, including Windows and some commercial Unix platforms. Follow the installation instructions found in the README file.