It's not always easy. Sometimes people give hints or act differently, but it's not a sure thing.
Well, it can be tricky. You might notice if they're secretive or guarded about certain topics, but that doesn't mean it's a private story for sure. There could be other reasons for their behavior.
It's hard to tell for sure. Maybe if they seem reluctant to share or become defensive when certain subjects come up, but it's not a definite sign. People have different ways of protecting their privacy.