After fighting with various parts of ALSA, PulseAudio, Skype and so forth trying to figure out why my webcam microphone wasn’t picking up any sound when trying to make test calls, I finally figured out the answer: when PulseAudio’s mixer for the input level on this is 100%, the device is actually muted (the why of that I haven’t gotten around to figuring out). If you leave the “Allow Skype to automatically adjust my mixer levels” box checked in the sound devices dialog of its options pane, it will set the input level to 100%, hence muting the mic.
To restore (or enable) sound recording, all you have to do is open up PulseAudio’s settings to set the input level on the webcam’s microphone to something less than 100% and make sure the checkbox mentioned above is unchecked/disabled. How you get to your PulseAudio configs may vary by distribution; there is a shortcut to them on the Skype preference pane and you can bring up the dialog from the command line by entering “pavucontrol”. The microphone settings will be on the “Input Devices” tab, and the mixer level for the webcam mic is the slider located in that device entry.