When you choose to install Mysql from the package selection menu during Fedora Installation, what gets installed apparently  is the mysql-client.  So  when you try to run mysqld at the shell, you may end up getting a socket error. This is because the main component mysql-server is not installed. You can install is simply my issuing yum -y install mysql-server at your root shell.

It will be 13MB download approximately. Then you should get the following when you attempt to start the mysql daemon.

[root@localhost ~]# /etc/init.d/mysqld start
Initializing MySQL database:  Installing MySQL system tables...
OK
Filling help tables...
OK

To start mysqld at boot time you have to copy
support-files/mysql.server to the right place for your system

PLEASE REMEMBER TO SET A PASSWORD FOR THE MySQL root USER !
To do so, start the server, then issue the following commands:
/usr/bin/mysqladmin -u root password 'new-password'
/usr/bin/mysqladmin -u root -h localhost.localdomain password 'new-password'
See the manual for more instructions.
You can start the MySQL daemon with:
cd /usr ; /usr/bin/mysqld_safe &

You can test the MySQL daemon with mysql-test-run.pl
cd mysql-test ; perl mysql-test-run.pl

Please report any problems with the /usr/bin/mysqlbug script!

The latest information about MySQL is available on the web at
http://www.mysql.com
Support MySQL by buying support/licenses at http://shop.mysql.com
[  OK  ]
Starting MySQL:                                            [  OK  ]
[root@localhost ~]# /etc/init.d/mysqld stop
Stopping MySQL:                                            [  OK  ]
[root@localhost ~]# /sbin/service mysqld start
Starting MySQL:                                            [  OK  ]
[root@localhost ~]#

Be sure to change the password, as users often tend to leave the default 'NO' password, thus making their database vulnerable.