At first is good to check Skype-version.

Open Terminal and run

apt show skypeforlinux

Install libv4l-0:i386

sudo apt-get install libv4l-0:i386

… probably installed already
… make a script

sudo nano /usr/local/bin/skypeforlinux

… a contents

#!/bin/bash
LD_PRELOAD=/usr/lib/i386-linux-gnu/libv4l/v4l1compat.so /usr/bin/skypeforlinux

… save and quit and make the file executable
Ctrl o
Ctrl x

sudo chmod a+x /usr/local/bin/skypeforlinux

Open Skype and check the camera.

########################################################################

With old Skype the process was almost similar.

sudo nano /usr/local/bin/skype

… a contents

#!/bin/bash

LD_PRELOAD=/usr/lib/i386-linux-gnu/libv4l/v4l1compat.so /usr/bin/skype

… save and quit and make the file executable
Ctrl o
Ctrl x

sudo chmod a+x /usr/local/bin/skype

Open Skype and check the camera.