Ah right - you want to record audio streaming from the internet and that kind of thing.
With WinAmp you don't need to record it - WinAmp can write directly to disk - it used to be called the "diskwriter plug-in" - I think it's now built directly into WinAmp. Basically, it just sends the audio data to your hard drive instead of to the sound card or headphones. This is faster than recording and better quality because it is not having to go through the sound card.
For recording from your web browser, you need to record from the "Stereo Mix" input of your sound card. It is unlikely that your headset will have the option of recording "Stereo Mix", but your normal sound card probably will.
To set the recording inputs you need to go into the Windows Control Panel and set it there. If you set "Stereo Mix" as the default recording source then Audacity will probably pick that up automatically when you next open Audacity. If it doesn't, then just go into Audacity Preferences "Edit Menu > Preferences > Devices" and set the recording device the same as you have set in the Windows Control Panel.
If you need some guidance making the Control Panel settings, see here:
http://wiki.audacityteam.org/wiki/Mixer ... es#vistacp
Vista has a few "peculiarities" that make it less than helpful for recording, especially for recording "Stereo Mix", but most of the issues that you may come up against are covered here:
http://wiki.audacityteam.org/wiki/Windows_7_OS
This section may be particularly relevant:
http://wiki.audacityteam.org/wiki/Windo ... d_playback