Source: http://fragments.turtlemeat.com/mysql-database-backup-restore-phpmyadmin.php

Backing up the SQL database

  1. Open phpMyAdmin.
  2. Get to your database from the drop down menu on the left. Click Export on the top of the page. Make sure that you have selected to export your entire database, and not just one table. There should be as many tables in the export list as showing under the database name.
  3. Select "SQL"-> for output format, Check the "Structure" and "Add AUTO_INCREMENT" values. Check "Enclose table and field name with backquotes". Check "DATA", check use "hexadecimal for binary field". Export type set to "INSERT".
  4. Check "Save as file". Do not change the file name. Use compression if you want. Click "GO" to download the backup file.
Restoring a backup of the SQL database
  1. Click the SQL tab.
  2. On the "SQL" page , unclick the "show query here again".
  3. Browse to your backup of the database.
  4. Click Go.