Many today at the university level do so by posting personal info on their web pages:
“I have students come to my office hours and comment on a commonality between their interests and mine,” he wrote. “For example, one student said they had sat in precisely the same spot as I had in the Italian Cinque Terre town of Vernazza.” Nate Ackerman, a lecturer in mathematics at the University of Pennsylvania, whose Web page includes information about his wrestling achievements and photos of him with his cats, agreed. “It’s better when your professor’s human,” he said."
Which is fine, though I don't think all professors should be forced into this kind of sharing. Our main job isn't to entertain or be our students' buddies. Another way to connect: watch, or at least be familiar with, some of the top/popular movies and TV shows that your students are washing. Try to know something about what they know about; be familiar with their world. Then we can speak some of the same language.
