On the old server, go to phpmyadmin, click on the database, click on the export tab, select all tables, export it to a file. Be sure the export does NOT include Create Database. You have to create the database manually here.

On the new server, if the file is not large, create the database under Mysql. Then click on phpmyadmin at the bottom, click on the database, click on the import tab. Browse to your file and import it. Be patient as it may take some time.

If the file is too large (more than say 5 megs), upload the file to your root folder instead and then email support@lunarpages.com and ask them to import it for you. Include the database name, file name and location, ownership verification.