Hi.
They emailed you all the information for the account probably just after paying (it's instant.)
Look for the nameservers in that account info email They're there.
they'll look something like this
ns10781.hostgator.com
ns10782.hostgator.com
there will be two of them.
Once you get those, copy them/open up another browser/whatever... go to godaddy. login. go to my domain name manager.
Click your domain name, then find and click 1 of the buttones that says something like "Change Nameservers" or "Update nameservers"
You'll click a circular checkbox that says Use custom nameservers (last option)
Then replace the two default ones that are already in field 1 and 2 with your godaddy ones, in order. the first one in the email as the first nameserver, second one in the email as the second.
Then click update.
Hostgator normally changes the DNS very quickly for me. But allow upto 48 hours for
http://www.yourdomain.com to become available.
You'll know once the DNS has propogated when you go to your domain name.com or whatever, and you DONT see the landing page/you see some hostgator default page.
Then use the file manager in your Cpanel login at
http://www.yoursite.com/cpanel (hostgator emailed you the info) and use the File Manager to edit/create your site.