I haven't done this in a while, and never on Windows, but I'll try my best to explain.
__________________________________________
1.) Open VLC on the source computer
2.) Go to File > Open Capture Device
I'm not sure on this next step, it's sort of operating system specific
3.) Select "none" for the video device (?) and select the proper audio device
4.) Tick the "Stream/Save" box, then click the settings button
5.) Tick the "UDP" box and enter the local IP address of the other computer. Take note of the port number (it should be defaulted to 1234)
6.) Click OK on both open windows so you're back at the main VLC window. If everything is working it should now be streaming. Play some music or something so you can get it set up on the other end.
...
7.) Head to the other computer, open VLC, and go to File > Open Network Stream
8.) Tick the UDP/RTP box, make sure the port is the same as it was in step 5
9.) Click OK. Hopefully you should hear your music playing from the other computer.
If the sound is choppy, go back to the Stream/Save settings on the source computer and selecting an audio codec. This should reduce the amount of bandwidth needed to stream your audio. I dunno how well your network will be able to support streaming raw audio, especially if you're using wireless.
__________________________________________
See if you can get that working. If you need any more help just holler. I might try this out myself in the next day or two just for kicks, so if you don't have it working by then I will probably be able to give you specifics.
@AtomicAudio: It depends on what transcoding options you set in the Stream/Save settings. If your network can handle it, it could theoretically be the same quality as the source. Again, I plan to try this soon, so I will let you know.