Make sure that you have installed the mysql-server, not the mysql-client or something else.
error means the file /var/run/mysqld/mysqld.sock doesn't exists
Hence
Install it using following command
sudo apt-get install mysql-server

But if the mysql-server is already installed and is running, then you need to check the config files.
The config files are:

The config files are:

/etc/my.cnf
/etc/mysql/my.cnf
/var/lib/mysql/my.cnf

Let the mysql use the /etc/my.cnf by renaming the /etc/mysql/my.cnf.
Then prob may solve.

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