How to set up an external IP address

EDIT: this is for outside of network access.

I'm configuring remote desktop access to my Ubuntu following this tutorial. However, after testing the connection, it doesn't work. I imagine it's because I never setup an external IP for my Ubuntu machine. :)

I don't have experience in this area, so I was looking to this article on how to setup an external IP address. But before I go ahead, a couple of questions. Is an external IP address, what I should be looking for? And do I need to have any security concerns by creating one?