If you can't see your friend's video, the problem is either with their video/webcam, or with your settings.
Check your privacy settings.
Go to Skype > Preferences and then choose Privacy. Under Allow video and screen sharing from, make sure that either Anyone or Contacts is selected. If you select Nobody, you won’t be able to see any video.
If you still can't see your friend's video, then it's likely the problem isn't yours. Recommend that your friend follow the steps in this article.