Would cognitive empathy not be prerequisite to affective empathy? How can you share in another person's emotions if you're not able to recognize them in the first place?
I guess evolved instinctive or subconscious behaviour - (INB4 someone says "mirror neurons" and then someone else replies "mirror neurons do not work that way!") but you know how watching youtube videos of people getting hurt in hilarious fashion causes us to wince? Like that.
Communication. I don't have a good script, but basically, ask questions. "What upsets you about it the most?" - that expresses understanding, compassion and offers a metaphorical shoulder to cry on. People love attention and talking about themselves, so they'll tell you.
