I think by far the easiest way to share files is to set up an FTP server.
Unless you want to share files through your Wordpress site. You will have to elaborate further what it is that you want exactly.
To set up an FTP, here you'll find a guide:
http://www.instructables.com/id/Raspberry-Pi-Web-Server/step9/Install-an-FTP-server/
On the other hand you could just make your Wordpress site host files.
I'm not very familiar with WP, but it's pretty customizable from what I have heard, given that you know some php etc.
Otherwise, you may want to give this a read as an alternative:
http://wordpress.org/plugins/wp-downloadmanager/
update:
Since it appears you want some kind of web interface, maybe have a look at this project like you suggested in your link: http://sourceforge.net/projects/webdisk/
A quick google found me this guide for the installation: http://blog.boreas.ro/2009/08/integratum-webdisk-on-rhel-53-x64-using.html
Or look around on github for a "webdisk" project that suits your needs the most.
EXTRA
As stated in another answer here, owncloud is also a possible contender.
However it doesn't run all that smooth on a Raspberry Pi, expect 3~5 second page loads with already optimised PHP.