If you cannot effectively ascertain what people are feeling and why they are feeling that way, you will not be able to address their concerns. A helpful activity for building empathy is to try reading people's facial expressions. Every day, try to ascertain what at least one person is feeling by looking at his face. After you have finished trying to guess that person's feelings, write your guess down in a notebook. This activity will get you to practice "tuning in" to people's feelings, which will in turn help you develop empathy.
Conflicts often occur when people have hidden agendas. If you are working with a group, you can teach a lesson about conflict resolution by conducting a game about hidden agendas. In this game, give each member a piece of paper with a list of his own objectives and a list of group objectives. The group objectives deal with building a house out of building blocks, and the individual objectives contain contradictory instructions. At the end, the house usually doesn't get built, because everyone is following contradictory instructions. At the end, resolve the conflict by telling everyone to discard their hidden, personal agendas and just focus on the group instructions.
Sometimes, conflicts break out as a result of verbal triggers rather than actual disagreements. For example, if one person uses a word another person finds offensive, that can start a conflict. One exercise you can use to practice your conflict resolution skills is to think of a conflict you have been involved with in the past week. Once you have identified the conflict, write the key words the person used that made you feel angry. Once you have the words down on paper, write a list of solutions you could have proposed but did not because you were angry or offended. This will help prevent your emotions from getting out of control, which will improve your conflict resolution skills.
You can use role-playing to simulate real-world conflict simulations. Simply write a scenario out on paper involving three fictional characters and a dispute over which one will get to take the day off work. Provide background information, such as which characters had taken the most days off prior to the disagreement. Either assign character roles to real people in your group (if you're working in a group), or write down a list of possible solutions (if you're working on your own). If you're having people act out solutions, ask them to come up with their own resolution ideas rather than relying on you for ideas.