This error means the file '/var/mysqld/mysqld.sock' doesn't exist. Verifie if mysql-server is installed (it's different from the mysql-client). But if the mysql-server is installed verifie that it's running. if not try restarting it using

service mysqld start

Verifie also if the file /var/run/mysqld/mysqld.sock exist. Sometimes the socket is installed there or try to find the file mysqld.sock using these commands:

updatedb
locate mysqld.sock

If this file exists then check the config file

/etc/my.cnf 

and modifie the socket file config value to match the location of the mysqld.sock.

This error means the file '/var/mysqld/mysqld.sock' doesn't exist. Verifie if mysql-server is installed (it's different from the mysql-client). But if the mysql-server is installed verifie that it's running. if not try restarting it using

service mysqld start

Verifie also if the file /var/run/mysqld/mysqld.sock exist. Sometimes the socket is installed there or try to find the file mysqld.sock using these commands:

updatedb
locate mysqld.sock

If this file exists then check the config file

/etc/my.cnf 

and modifie the socket file config value to match the location of the mysqld.sock  .