First, you must download the software.
Head on over to http://www.mysql.com; click the "downloads" link, and choose the latest "stable" release.
I prefer to get the source packages rather than the binary packages. This way, I get to see more of what is going on with the installation and feel that I have a little more control. These instructions cover installing MySQL from a source package.
Download the source package, and put it into a directory where you can extract the .tar file.
Extract the source files.
tar -xzvf mysql-3.23.xx.tar.gz
As root, create the group and user for MySQL.
groupadd mysql useradd -g mysql mysql
Switch to the directory where the source files are located; this directory is created when you extract the files.
Run the configuration script.
Compile the source.
Install the files.
Install the initial databases.
Change the ownership of the MySQL files.
chown -R root /usr/local/mysql chown -R mysql /usr/loca/mysql/var chgrp -R mysql /usr/local/mysql
Copy the configuration file to the /etc directory.
cp support-files/my-medium.cnf /etc/my.cnf
Start the MySQL daemon.
/usr/local/mysql/bin/safe_mysqld --user=mysql &
MySQL should now be up and running for you!