OK I'm guessing you have the program installed and running, and that you've found the round red circle that's labeled "Record (Ctrl+

."
The window that comes up needs a filename and location for the recorded stream. Use the name of your favorite pet, or call it AuralMoonStream. Or whatever you want.
The "Format" section is a bit misleading. No matter what settings you choose there, it will still record a WAV file. You can just make them sound better or worse (but of course no better than the quality of the actual stream.) The default settings are standard "CD Quality" so unless you're going to be burning the stram to DVD-Audio or you have serious disk space constraints, leave that part alone.
The "Device" setting might have a couple choices of soundcards in the dropdown, depending on your hardware configuration. Pick whichever one you're using. The "Microsoft Sound Mapper" is nothing special, it's just a fancy (or not) way of saying "whatever the default device is." If you have the MSM and only one other sound card listed, either one is fine because they're the same thing.
What's important here is that you have that device set up properly. If you've got a little gray speaker in the system tray (bottom right, near the clock), you're set. Double-Click that. If you ain't got that, you just need to take the long way. Click Start

Control Panel

Sounds and Audio Devices (in Classic View)

Advanced (on the Voice tab under "Device Volume").
No matter how you got here, you should now have a window open called "Volume Control" and it's got sliders and such. Click Options, then Properties. Then click the radio button next to Recording. See the check boxes below that? Look for one that says "Stereo Mix" or "What You Hear" or "Sound Card Output" or something like that (it varies depending on your sound card.) Make sure that one is checked. Hit OK.
Now you're back to the sliders, except these are the recording sliders, whereas the others were playback sliders. Check the one below "Stereo Mix" or "What You Hear" or "Sound Card Output" or whatever you just found on the last screen. Adjust the volume appropriately. If it's all the way down you'll be recording silence, which is arguably less interesting than GY!BE. The disk space wasted by recording silence is... well I'm digressing.
So you don't know where the volume slider should be? It depends, but about 90% should be safe. Here's a trick... you can leave this window open and go back to CD-Wave.
If you'd like to set up your Voice Activated Start or Schedule Recording, feel free to do that at this point. Let's say we're running a test to make sure this works. We've got our file name and location, proper soundcard selected, and so on. So we'll hit "Start" when Aural Moon is playing something particularly cool.
A waveform starts delevoping in the CD Wave window! Here's where you can adjust your recording and playback volume to fit. Too loud will sound bad, too soft will be... soft.
Done? Wanna stop? That's the black square. There you go. You're done, your stream is recorded. The save button will allow you to save it as an mp3 if you desire, or split it into tracks before you try to save it.
NOTE: If you have anything else running that makes sounds (instant messengers, email checkers... anything) and one of them make a sound while you're recording, you'll get those sounds on your recording too. Best to disable sounds on all your other programs or leave them closed, unless you like the sound of (Geddy Lee voice) "Searching for the lost [You've got mail!] Xanadu."
OTHER NOTE: I hope this doesn't come off as condescending. I deal with some people at my job who need things done step by step or else they're lost. Thinking for themselves is not an option. Therefore, I must write tutorials in this manner.
I followed these instructions and ended up with a nice recording of the Aural Moon stream. If it's not working for you, it's YOUR FAULT!
