How to access "Stereo Mix" recording in vista?

Go to the windows Control Panel, open Sounds. In the Recording tab, right-click and choose Show Disabled Devices. Stereo Mix will appear (amongst other). Right-click Stereo Mix and choose Enable.

You might want to have a look at the device properties (right-click > properties) for volume and other settings.

You would probably still need to set the recording program you'll be using to use the Stereo Mix as a recording device.

One alternative is to use a recording program that supports the Vista API specifically. The Vista audio API (aka WASAPI) allows a compatible program to capture the sound that goes to your speakers. This has the same effect as selecting Stereo Mixer as your "Record" device had.

Example in Audacity:

That's all there is to it. Record Skype, websites, games - whatever. Anything that goes to your speakers, goes into Audacity too.