The instructions below are for Install Let's Encrypt on Apache. You may also want to check out how to Install Let's Encrypt on Nginx.
Here you can find instructions for how to use Let's Encrypt's Certbot with the Ubuntu 14.04 and Apache setup we use with Livecode Server - certbot.eff.org 
Which created the following conf files:
000-default.conf 000-default-le-ssl.conf
In the directory:
/etc/apache2/sites-enabled
which in term is usually sym-linked to files inside:
Note: the reason for having to manually edit the 000-default.conf file was because it over-rides thenewly created 000-default-le-ssl.conf file that
/etc/apache2/sites-available