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Go into your PHPMyAdmin (should be in the control pannel on your host) and backup your tables from your database to your local drive. Using FTP copy your sites contents to your local drive.
Once youve done that create a database on your new host with the backup tables you created earlier, (using phpmyadmin on your new host control pannel) upload the sites files to the new host using FTP, edit your mainfile.php to make sure the domain is correct and the path to your database etc is all ok.
Easy, your done....