Like I learnt from a person on irc freenode on channel #videolan..
(I've also gone to http://wiki.videolan.org/Documentation:Streaming_HowTo which seemed helpful)
I should use one instance of vlc to stream to a file, while I launch another instance to stream that file. Ok, why not? Here's how I (try) to do it:
From menu "File" I select "Open Network Stream... Ctrl-N"
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Without me doing anything, "UDP/RTP at port: 1234" was already selected. The only change I did was to check the checkbox "Stream/Save", then I clicked on Settings, just as is marked on the image.
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Then I click on "OK" again.
This is what I've done so far.