I managed to do this for VLC 0.99 but not with the latest VLC 1.0.5
I have tried to follow the advice in
http://wiki.videolan.org/Documentation:Streaming_HowTo
and also from other webpages but such advice seems dated, it seems that VLC's GUI has changed.
VLC says that it is "streaming" but I don't have any evidence that it is. I have looked in Media Information > Statistics and see that the Input figures are changing but the Streaming figures are 0.

My firewall does not list VLC in it's real time connection monitor which suggests that VLC is not listening nor streaming to any port.
I was not able to stream any MP3 files. I am not even sure if the "stream" and the playing MP3 operations happened together, i.e. I could supposedly stream but not get MP3 into that stream, so it was an empty stream - this I assumed from reading the Playlist.
I used the "Capture Device panel" with "DirectShow" to capture from a webcam and that seemed to stream, VLC said it was streaming, but again no output was actually detected. I tried different ports and protocols. Nothing seems to work.
Any advice on how to detect if VLC is streaming or just claiming to stream? That would be a good place to start.