This tutorial covers installing MySQL server and client, as well as some basic configuration to get you up and running.
Install MySQL service and command line tools.
$ yum install mysql mysql-server
Once thats done turn on the MySQL service so that it automatically starts on boot.
$ chkconfig --level 2345 mysqld on
Finally start the MySQL service.
$ /etc/init.d/mysqld start
We are going to open up ports 3306 in iptables.
$ vi /etc/sysconfig/iptables
Add the following lines (make sure its above the reject statement).
-A RH-Firewall-1-INPUT -m state --state NEW -m tcp -p tcp --dport 3306 -j ACCEPT
-A RH-Firewall-1-INPUT -j REJECT --reject-with icmp-host-prohibited
Restart iptables service for changes to take effect.
$ /etc/init.d/iptables restart
That completes the steps to install mysql, from there you can login in through the client to setup whatever you need to.
$ mysql -u root
On a side note in some odd cases there may be issues with the database instantiating. You may need to create the database manually.
$ mysql_install_db --user=mysql --basedir=/usr/ --ldata=/var/lib/mysql/