It depends on how you are exposing this externally. You will probably need to setup your AAMs like so (using foo.com as the FQDN example)
Load you SSL certificate compatible (like a wildcard cert of *.foo.com) for https://mysite.foo.com into IIS and assign the certificate to the IIS web site. You will also need to ensure that in your bindings in IIS you have the host header entry for http://mysite.foo.com
After that your either going to be doing a NAT at your firewall to send traffic to the SharePoint server hosting the site or your using Forefront TMG (preferred) and setup a rule - try the SharePoint Publishing wizard.
Theres a fair bit too it I can provide more information if you tell me where your not getting any luck from. I suggest testing it internally by first getting the SSL certificate installed for the site, setting up the AAMs and putting the entry for the FQDN into your hosts file and ensuring you can then access the site.