Understand your own emotions. To increase your empathy, you need to start with yourself. Pay close attention to your emotional state, noting what situations change your emotions, what gives rise to positive emotions and negative emotions. Use this material as a point from which to understand others' emotional responses.
Interact with a wide range of people. Get to know people of all ages, ethnicities, sexual orientations, socio-economic backgrounds and levels of physical ability. The more types of people you get to know, the more experiences you will have to draw on as you try to increase your empathy.
Seek out similarities between you and others. When we stress difference between ourselves and other people, it's much more difficult to understand others. Especially seek out the similarities between you and people you do not like or who you disagree with. For even greater empathy, seek out the similarities between you and other species.
Practice taking on another's perspective. Train your mind to be open to perspectives other than your own and evolve to actually immersing yourself in a different perspective. For example, if you are pro-life, take on a pro-choice stance to better understand the other side. You can do this on a personal level as well and it doesn't have to just involve moral and political ideas.
Examine the lives and work of famous empathetic people. It's easier to become more empathetic when you have good role models. Choose people deeply involved in a social cause you respect and read biographies to better understand how they used their empathy.
Read good fiction. Recent studies have shown a connection between reading fiction and gaining empathy. Fiction generally contains accounts of individuals' difficulties and being exposed to emotionally evocative material can help you better understand people's internal states.
Foster empathy in your children and in those around you. Respond to children you are close to in a non-authoritarian way, reasoning with them about the effects their behavior can have on others. Let children know that it's in their nature to be good, sharing members of a community.