I'm the pioneer of internet radios kept by drunkards. (Naturally drunk at the moment)
www.shoutcast.com
From there get a server and broadcasting plugins. You need Winamp 2 or 5. Start the server and then start the plugin. In the plugin window select source (sound card input preferred) and start the broadcast. Now the Winamp broadcasts the input from your soundcard (the input which is set in the control panel -> audio).
I run my radio via NI Traktor. I have a speech background music on the deck A and the songs are on the other deck. I run the Traktor output to mixer where I mix the music with speech and then I rout the mixer signal to sound card input. Traktor is really nice program for internet radios. Easy crossfades and other stuff.