While not as common as the "why medicine" station, conflict resolution stations are by far the most interesting station for an interviewer. Why you ask? Well that's easy, it's because most interviewees give dumb answers. Can you relate?
What Not To Do
100% of the time the stem will be worded in a way that for most people, will skew their perspective a specific way. If you follow that perspective after you have read the stem and start accusing this person of this and that, guaranteed the interviewer will not look favorably upon you and it'll become a wreck of a station.
What To Do
1) Analyse the situation/conflict. i.e. Who, What, When, Where and How.
2) Consider the conflict from all the stakeholders point of view i.e. potential thoughts and feelings.
3) Understand your role in the conflict, you might be a 3rd party to the conflict.
4) Determine what the endpoint to the conflict should be. Whether it's just to calm someone down or a complete resolution of the issue, the approaches might be similar but what is said will be different.
5) If it's an actor station, just do it but if it's just a stem and you just talk about the scenario to the interviewer, than take the interviewer through your thought process, explain what you would do and how you hope/expect things will go.
Some conflicts that have arisen over previous interviews have been when you are a junior intern and have to ask a grumpy old doctor for extra work he becomes heated. By always looking to calm down the situation and looking for alternate ways in which to benefit both parties may also be a great way to resolve the conflict.