Sounds like a typical permission problem, you need to ensure that your permissions can correctly read and write the database sock file.
If your file my.cnf (usually in the /etc/mysql/ folder) is correctly configured with:
socket=/var/lib/mysql/mysql.sock
You can check if mysql is running with the following command:
mysqladmin -u root -p status
Try changing your permission to mysql folder. If you are working locally, you can try:
sudo chmod -R 755 /var/lib/mysql/
If the above doesn't fix the problem then its likely something else, Visit Can't connect to local MySQL server through socket '/var/mysql/mysql.sock' (38)Can't connect to local MySQL server through socket '/var/mysql/mysql.sock' (38) on Stack Overflow for more answers.