where did you buy your domain? with hostgator or from another registrar?
in case you didn't buy it from hostgator you need to go to your registrar and enter your hostgator dns settings ( usually something like nsxxx.hostgator.com and nsxxy.hostgator.com ) this will bind your domain to that specific hostgator server
Hostgator sends you an email with your cpanel password and other stuff, there you find an IP address, that is a number like 123.123.123.123, that's the IP of your server.
In order to check if you need to apply the dns settings launch the windows shell ( DOS, call it as you prefer ) and type: ping yourdomain.com
if it tells you it points to that same IP address you don't need to do anything of the above, otherwise you know what to do.
You can upload your files via FTP as well entering that IP in place of ftp.yourdomain.com, but you need to properly set your dns servers in order to make your domain reachable...