All you need is a 1/8 audio cable. Any radio shack, walmart, hell even walgreens has them. I'm using one from Radio Shack that is gold tipped. Probably overkill though.
Plug one end into the speaker out jack of your scanner, and plug the other end into the LINE IN or MICROPHONE jack on your PC.
Scanamerica can provide you the software you need to stream, and Gordon (owner of scanamerica) will give you instructions on how to configure it to work with his feed. Then all you have to do is just either click the connect or disconnect button on the software which sends the audio to his icecast server, or unplug the cord from the scanner so no audio comes out.
Personally I don't know why anyone would only want to run a scanner part-time. I mean unless you absolutely need the line-in or mic jack on your pc, running a scanner does not take any bandwidth away from your connection, and the software runs in the background so you don't have to have anything up on your screen. The only limitation is needing to keep the scanner and PC on all the time.
I use an old beatup laptop computer. It had been sitting in the closet for a few years not being used for anything and I decided to make it my dedicated FEED machine. It worked out well. So I can turn my pc off and on as I please and it not disrupt the feed.
here ya go:
http://www.myradiostore.com/p/6-foot-1-8-inch-stereo-cable.html