What mechanism is used to access MyCloud Live over the Internet?

You can use inadyn for DDNS on the MBL: http://www.inatech.eu/inadyn/

You’ll need an account with some DDNS provider. I’ve used no-ip, but they’ll nag you every month to refresh the (free) account.

Enable SSH for secure remote access/file transfer. http://community.wd.com/t5/My-Book-Live/What-are-the-steps-to-enable-SSH/td-p/324417

However, you will need to open the ports in your router yourself in order to access the MBL from outside your local network.

optional: If you are behind a router that is not under your control, but have access to a Linux machine somewhere on the internet, you can use autossh to forward a connection to that machine instead, and log in to your MBL via that remote Linux server.