Pretty much everything 2niner2niner said is true, but i ran into a few problems with SQL compatibility (ERROR 1062 (23000) at line XXX: Duplicate entry 'XXX' for key 'PRIMARY'); and rather than zipping/extracting and wasted steps you can:
- Login though FTP and download your wordpress directory
- Backup your Database through myPhpAdmin to SQL (Required Settings: UNCHECK "AUTO_INCREMENT" under create table options, and CHECK "Truncate Table before insert" and "INSERT IGNORE statements". Optional: Select the datatbase system compatibility)
- Install wordpress on new site
- Upload your backed up wordpress directory over your new install
- Update settings in wp-config.php (check wp from your new install, if installed through your server or script it might already have the settings you need)
- Import your SQL dump
- Update your DNS settings to reflect your new site
Enjoy!