Here is a dictionary definition of empathy from reference.com:

em•pa•thy   –noun

1. the intellectual identification with or vicarious experiencing of the feelings, thoughts, or attitudes of another.
2. the imaginative ascribing to an object, as a natural object or work of art, feelings or attitudes present in oneself: By means of empathy, a great painting becomes a mirror of the self.

Here’s what Wikipedia says about Empathy:

Empathy is the capability to share and understand another’s emotions and feelings. It is often characterized as the ability to “put oneself into another’s shoes,” Empathy does not necessarily imply compassion, sympathy, or empathic concern because this capacity can be present in context of compassionate or cruel behavior. Read more…

And here’s what the Center for Nonviolent Communication(CNVC) says about the practice of empathy:

Three ways to know you’re in empathy (i.e., making the connection):

1. Intention.
   Be aware of the intention behind offering empathy to another person. It’s important that you be conscious you’re not giving empathy for the other person’s benefit. Don’t listen unless it meets your need to connect with the divine energy.
   By that, I mean that to know God*, we have to know people. It’s a deep need, our need to connect with the beauty, the divine energy in this person, to be in harmony, to flow with that divine energy.We give empathy to others for our own benefit. With this intention, you can’t tell which is the giver and which is the receiver. We don’t do it for the other person, because that puts them in the one-down position of being helped. There is life coming through this other person, and we meet our need by connecting with it.
2. Presence.
   This means we can’t bring anything from the past chattering in our heads, such as theories about humans. The more you know the person in front of you, the harder it will be to empathize. That’s why Martin Buber says our presence is such a precious gift to give another. It’s approaching this moment like a newborn infant. That infant has never been before and will never be again. I learned this when I worked in mental hospitals and found that the best way to connect with the patient was not to read any of the reports.
3. Focus.
   The focus is on what’s alive in the person now in this moment. The best way to do that is staying connected to feelings and needs, especially the past feelings that are the root of the present feelings. The person may be wandering around with reference to past, memories, etc., but you don’t go there with them. Just stay connected to the needs and feelings behind what they’re expressing.

All of this can be done silently. The most important parts of empathy are done silently.

*When I mention God, I understand that many readers may be non-theistic or even anti-theistic. These words come from Marshall Rosenberg, founder of the Center for Nonviolent Communication. I include them because I wish to be inclusive, accurate and complete, and am not troubled by the idea or belief in God. Learning empathy is not dependent upon believing or not believing in God. Personally, when I use the word God, I mean “ultimate reality” or the “ultimate unknown.” I recognize that for some people, God is a being who resides in a heaven, for others, the ultimate might mean Emptiness or Buddha nature, or perhaps Nature itself, Science, or Goddess. To reiterate, empathy can be practiced and learned whether or not we believe in God as a supreme being, practice non-theism, or any of the spectrum of other possibilities. —Editor