Yes, this is possible
The guide you linked shows you how to do 3 things: Install and set up FreeNAS, Port forward your router, and up a dynamic DNS service
Install FreeNAS
I assume you're able to do this part, but here's a video anyway:
(The main video starts at 0:47)
Port forwarding
If you've never port forwarded a router, this can seem complicated at first, but it really isn't once you get the hang of it. Port forwarding allows you to connect to your NAS whenever you're not connected to your home network. http://portforward.com/english/routers/port_forwarding/ has guides for most routers, and if you can't find the exact model you have, try something similar as the process will probably be similar within the same manufacturer.
Note: There does seem to be an ad that pops up every now and again for a software utility that can port forward your router automatically, just close it. It really is simple to do it manually
Dynamic DNS
This just makes it easier to remember your IP address (instead of typing in something like 281.232.281.656 you could just have is be a URL like example.no-ip.org or example1.dyndns.org depending on the provider you go with.) I use noip, and here's a guide for it http://www.noip.com/support/knowledgebase/getting-started-with-no-ip-com/ although most services will have a similar setup process
Since this will be visible from the internet, you'll want to choose a strong password (I hope this is obvious, or at best just slipped to the back of your mind) Also, you might want to consider what @braneopbru has said, owncloud is pretty simple to set up and is pretty secure
I hope I haven't left too much out of this post, and if you need any help just PM me, and I'll try my best