To record both sides of a Skype conversation you need special software.
For suggestions of suitable software, see: https://forum.audacityteam.org/t/blank-spots-recording-skype/34380/2
For recording sounds that are playing on your computer, assuming that you are using the current 2.0.5 version of Audacity and are using Windows Vista or later, use the “WASAPI loopback” option as described here: http://manual.audacityteam.org/o/man/tutorial_recording_audio_playing_on_the_computer.html