The quick and dirty way to backup (dump) all databases currently served on the server:
I assume the server is not running any GUI, right at the command line, type the following:
sudo mysqldump --all-databases > /home/username/dumpalldb.sql -u root -p
where:
username = home folder for the user currently logged in.
dumpalldb.sql = the sql file dump of all databases.
dumpalldb.sql = the sql file dump of all databases.