If you’ve accidentally closed the video preview window in Skype, it should re-open next time you start a call. If not, you can re-enable it by performing the following steps:
Go to Tools > Options, and click on Calls. Click the Show Advanced Options button, and uncheck Show call controls when Skype is in the background.
Now, hover in your call window, and you should see a new icon in the lower-right corner that looks like a square. Click that, and there will be a menu item for Pop-out video. Click that, and the preview window will appear and stay on all the time.
Tested on Skype 220.127.116.11