Backup all files in /var/lib/mysql to another folder
To restore, stop mysqld if it is running
service stop mysqld
Move all database files back to /var/lib/mysql. Make sure that all the folder and files in that folder belongs to mysql
chown -R mysql.mysql /var/lib/mysql
Try starting mysql
service start mysqld
I use this method only after an OS reinstall. There are easier ways to do a simple database backup.