the RPM install should:
- copy the MySQL binaries to appropriate locations on your system (usually, binaries go to /usr/bin and /usr/sbin, while databases and tables are stored in /var/lib/mysql)
- add appropriate entries to your system’s startup scripts so that the MySQL server starts up automatically at boot time
note that the MySQL database is running on your Linux system is the "mysqld" process is running. "mysqld" is the MySQL deamon server process. you interact with the MySQL server via the command line using "mysql" or a host of other MySQL commands such as "mysqldump", "mysqlcheck", etc.