Focus on the issues, not the person. Keep the focus on the problem being discussed, not on personal issues. Do not take a complaint personally. This reassures the student that you are listening to the complaint and it ensures that both parties understand the problem. Anger vs. Fear.
Some upsetting behaviour stems from students' fears, such as the fear of failing.
Be insightful about such possibilities and try to get at the root of students' concerns by asking questions. Focus on fairness. This is particularly important when the conflict arises from a grade complaint. Re-establish the class grading criteria, and have an example of an A paper for students to read. Look at the work.