Many times this goes hand and hand with secure certificates. Secure certificates are usually applied to either the FQDN (Fully Qualified Domain Name) and/or the web server.
You can generate your own secure certificate, however if this is for public consumption then you will most likely need to spend some money and get a certificate from a Certificate Authority such as GeoTrust.
Once you have the secure certificate setup on the domain/web site then it is usually a matter of making sure that the ports (default SSL is 443) is mapped to the correct web site/domain.
After all of that you can access the content via HTTPS and HTTP. If you want to only allow HTTPS then you will need to do change some web server configurations/settings.
Usually the Certificate Authority has start to finish instructions on how to get the certificate installed on common web servers such as:
IIS (Internet Information Server by Microsoft)
Start to finish you can usually get the secure certificate from a Certificate Authority within a few hours or less.
Usually commercially available secure certificates have an expiry date. Generally if you pay more the certificate last longer, but this is not always the case.
“The strongest of all warriors are these two — Time and Patience.” ― Leo Tolstoy, War and Peace