“A soft reply turns away anger.” (Proverbs 15:1)
When you communicate to others in a soft manner, this will calm someone who is already angry at you. This refers to both your tone of voice and the content of what you say. Be mentally prepared to apply this to someone who is likely to speak to you in anger.
When the person who is angry has a valid complaint against you, admit that he’s right – and this will calm him down.
Sources: see Vilna Gaon – Proverbs 14:30 and 15:1; Rabbi Zelig Pliskin – “Consulting the Wise”