wblz what kind of hosting are you using ? Shared hosting, managed VPS or a custom setup ? What webserver are you using ? Apache/Nginx ?
Moving from a domain to another will depend on all that. You might also want to check your admin panel documentation if you're on cPanel or similar and unfamiliar with subdomain management.
If you have the knowledge to install it from scratch on a subdomain, you should be able to guess where to move your existing files ?
If you have SSH access I suggest you move files via mv, it will probably be done instantly compared to using a FTP application.