WordPress has terrific documentation on their website about Backing up Your Database that will help guide you through this process. You can go ahead and do this one of two ways: directly executing mysql commands on the command line, or using PHPMyAdmin.
mysqldump to back up from the command line is simple, though you will need to know your host name, database name, and user name/password. A full explanatation for using
mysqldump to back up a database can be found at MySQL.com
Log in via the command line, and change directories to the directory where you want to save your database file. To create a file called
omeka_db_backup.sql with your database, use the following.
mysqldump -h localhost -u username -p omeka_db_name > omeka_db_backup.sql