i guess yum install mysql or yum install mysqld can do it as well

PS : here are some simple steps

Code: 
yum install mysql-server php-mysql
Code: 
/etc/init.d/httpd restart
Making MYSQL

Code: 
mysql_install_db
Fix some permissons :

Code: 
chkconfig --levels 235 mysqld on
Restart Mysql

Code: 
/etc/init.d/mysqld restart