I'm still learning a lot about conflict and how to deal with it in a way that is loving, honest, and dignifying toward others. I imagine I'll be learning about that until glory; I certainly hope I don't STOP learning about it!
That said, I've picked up a thing or two about communication during times of conflict that I think are helpful. Here are a few thoughts:
Don't tell someone how they feel. Instead, tell them how YOU feel. I've heard people tell others something like, "You're angry..." or, "You're upset..." I've never seen this produce helpful results; if anything, the one being addressed usually does NOT feel the way they are told that they feel, and now they also feel misunderstood and defensive. The truth is that only you know how you feel, and only I know how I feel; if I try to anticipate their feelings, I'll probably get it wrong.
I recently had an interaction with another pastor who had been presumptuous in dealing with a particular circumstance in which we both had a part. I was frustrated, confused, and unsure how to deal with the aftermath of his presumption. I know that, often, frustration or confusion on my part comes across to others as anger. It was so helpful that my fellow pastor said, "I feel like you have withdrawn from our conversation, and I don't know if I've done something to upset you." That opened a door for me to communicate how I was feeling, and invited me back into collaboration with him. We stopped being adversaries and started being partners again.
Don't just listen to what they are saying. Instead, also listen to what they are telling you. We can use a lot of words when in dialogue about problems before us. Sometimes, those words can suggest things that are only a part of the story. I was once a part of a team that was giving counsel to a leader in authority who was dealing with someone who had acted wrongly; that authority figure asserted that he was trying to do things "by the book" and handle the offender accordingly. However, this leader had inadvertently run rough-shod over the other person, who had been open to correction and repentance before they were so caustically mis-handled!
I was grateful for the wisdom of another member of our team who lovingly pointed out to this leader how it was possible to "do the right thing in the wrong way." The authority figure wouldn't hear it, though, and we had to listen to what he was telling us beyond his words: he was unwilling to do things "by the book" if that meant that his authority would also have to include dealing lovingly with those under him. Sometimes words alone will actually mislead, but there is a larger message to be heard.
Don't judge circumstances (or people!) in the moment alone. Instead, assess them in context. I have faced problems with others that we focused on very precisely, and we worked out a great amount of detail about them. We may have arrived a a fair grasp of the immediate consequences of a problem, but often later learned that there were more factors involved than we took into consideration. This is often the case when someone has a very strong reaction about something, and our inclination can be to take that reaction at face value, in isolation of other factors. Consequently, we draw conclusions about the circumstances (and the person reacting to them) that are based solely on that moment.
I was in a meeting once where one member of a team checked another with a strong rebuke that, to the recipient, sounded like an unfounded accusation. The "accused" was so upset that he left the meeting. Afterward, in a conversation with a few of us, the "accused" man was clearly angry at the man who had rebuked him-- but we reminded this man of the other man's character, which was not that of a rash, accusing, and belligerent person that this man had determined him to be in the moment. In the larger context, those circumstances took on a different light.
Those are a few lessons I've learned-- sometimes the hard way!