Accurate empathy involves more than just the ability of a person to sense another's "private world" as if it were his/her own. It also involves more than just a person's ability to know what the other is trying to say. Accurate empathy involves one's sensitivity to the feelings of another, and one's ability to communicate this understanding in a language that the other person can understand.
It is not necessary that the individual feel the same emotions. It is instead an appreciation of sensitive awareness of those feelings. Essentially, you need to see the world through the other person's eyes and show that person that you are doing this.
Empathy gives a message that "I am here with you." The actions of the person must be in concert with the other person's mood and message. Empathic remarks comfort and encourage one to continue to talk.
Empathy is communicated by words as well as voice, body language, etc. All of these combined, demonstrate sincerity.
What Empathy Is Not
What True Empathy Is