If you get this error message when trying to use mysql command line utility from shell:
Can’t connect to local MySQL server through socket ‘/var/lib/mysql/mysql.sock’
It means you need to access the mysql using -h 127.0.0.1 e.g.
mysql -h 127.0.0.1 -u yourdbuser -p yourdatabase
If you get this error message from a web script, please check with support for the status of the mysql server.