Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock'

Maybe the MySql service is not active.  To check the status you can use the command below:

sudo service mysql status

If your MySql is not active, you can active it by command below:

sudo service mysql start

To restart service:

sudo service mysql restart

To stop service:

sudo service mysql stop

I hope it useful for you.

I got the same error, you have to reload apparmor setting. You can run commands as below:

sudo service mysql stop 
sudo /etc/init.d/apparmor reload
sudo service mysql start

Run line by line command, and finally run mysql -u root -p command to access to MySql CLI. If you can access it, your issue is resolved.