How do you record a Skype conversation on Windows?

I use MP3 Skype Recorder.

The MP3 files can be edited using Audacity.

You can use Audacity, and select the "Wave Out Mix" for the audio input. This should record your Skype call.

Call Graph (here) is one of these apps.

Some other inexpensive apps - Hotrecorder, Pamela, Freecorder

Call Graph, which is also free, works fine, and it even saves a dual-channel recording if you set recording as stereo (wave or mp3).

Then, you can split and then edit, save or just hear separately each of the channel (ideal for an interview and other purposes where the two voices may overlap and need to be separated) if you open it in Audacity and then split the stereo track.