I apologize for not being more descriptive. In PhpMyAdmin you'll see a left menu that lists your databases. Click the database containing ListMail. In the main window you should be presented with all of the ListMail tables. These, and the data they contain, (Click "Browse" on any table to see its data) are what need to be saved. At the top of the page you should see a button "Export". Click this button. On the Export page, select all of the ListMail tables in the select box. Choose the option "Complete Inserts" and "Create ZIP file". Leave the filename at the default, which should be a variable for the database name. Submit the form. Once created, save the file to your hard drive and you have all of your ListMail data backed up.
Restoring the data can be done through ListMail. Rename the unzipped version of the backup to have an .LM extension, upload it to your main ListMail folder, and use the ListMail Restore feature.
Hope this helps!
Regards