Hello Facetimecamera,
FaceTime is a great feature, and it's very important that the camera works in FaceTime as expected. If you're using FaceTime on a Mac start by force quitting any application that may be in use that has used the camera. You can force quit apps by clicking the Apple logo towards the top-left, followed by Force Quit. Once there click on the applications, followed by Force Quit. You'll want to keep Finder running. If you continue to have issues after those steps please restart the Mac using the steps in the following article.
Log out, sleep, wake, restart, or shut down your Mac
If restarting the Mac doesn't resolve the issue please test to see if the issue continues if you boot the Mac in to safe mode as outlined in the following article.
How to use safe mode on your Mac
If you're having issues on an iPhone, iPad, or iPod touch please restart the device, and confirm the device is updated. You can find those steps linked below.
Restart your iPhone
Restart your iPad
Restart your iPod touch
Update your iPhone, iPad, or iPod touch
Have a great day!