Suppose your webcam is in /dev/video0.
1. sudo apt-get install v4l2loopback-dkms
2. sudo modprobe v4l2loopback
3. Finally, when you need your webcam on Skype, just run this command:
ffmpeg -i /dev/video0 -vcodec rawvideo -pix_fmt yuv420p -threads 0 -f v4l2 /dev/video1