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The process for migrating Magento will involve:

• Set up the LAMP stack on a new server.
• Use PHPMyAdmin or mysqldump to export your database to a .sql file.
• Using the command line client, create your database with the same name on your new server.
• Import your data from the SQL file
• Copy your web files from your old hosting account (the contents of public_html) to /var/www/html on your new server
• Modify Apache to support rewrites by changing AllowOverride None to AllowOverride None in your site's configuration in /etc/apache2/sites-enabled/
• Restart apache with service apache2 restart