I practice empathy by roleplaying; it forces me to realize the constraints around the character, regardless of how far apart they are from me, so I can react appropriately to the constructed world.
I also watch a lot of movies and read lots of books, taking 'characterizations' from the people presented there. I imagine their faces, the movements they make, the words they say, when put into particular scenarios. This requires great attention to detail and good pattern-matching skills.
When creating a proper roleplay response, I always have a picture in my head of what's going on, and why, and what the person is feeling. I make the feeling my own, which, at the height of the role, allows the character to surprise even me.
Empathy is a huge life skill, useful in almost every interaction with other people. But, many people aren't able to empathize with others as effectively as they might want to. The standard technique is "put yourself in their shoes," which works for me. However, this doesn't always work with people completely different from myself, because I can't imagine reacting the way they are.
Does anyone have suggestions for how to "practice" empathizing, tips on how to do it better, or different techniques entirely?