First you need to check if the camera is properly installed in Device Manager. You can access Device Manager from Start > Run > devmgmt.msc. If it's not installed properly, you will see a yellow sign. Once this issues has been checked, open Skype and go to Settings > Video. Make sure to select the camera and test it from the same location. Next time you will place a video call, it will start automatically.
Alternatively, try updating Skype to its latest version by downloading a new package from its official website.