This really depends on what NAS you have, but looking at the standard consumer NASs that Lacie do, I can't see any that have a built in webserver that is capable of what you want to do.
Many support FTP and if you want to enable this for others to access your files, you simply need to forward FTP ports on your router to be forwarded to the IP of the NAS. Others will then be able to connect to your NAS by typing ftp://your_outside_ip - or by using the ip with your favourite FTP browser.
As for the webserver part, you can always install a webserver on another machine and use the NAS as the file store, but I do not think you will want to do that. If you do, again, you will simply need to forward HTTP/Port 80 from the router to the webserver.