Misunderstandings can occur not only in conflict situations but also on a regular basis, during ordinary conversation. Sometimes misunderstandings are verbal when people mean different things under one word. In the other cases, misunderstandings can be provoked by body language, intonation or emotions.
So, depending on the kind of misunderstanding you have, you can use different strategies. Of course, the best way out is clarifying the issue, before it gets serious. Once you notice that the person you are talking to did not understand something, you can repeat yourself in a more clear manner, speak up or simply ask what was not clear.
When it comes to strategies, it means that the misunderstanding has already grown to a conflict that needs a solution. I would point out three important points in this case: distress handle, getting help and offering help (if you appeared to be an observer).
Distress handle means holding back your emotions when you get angry with your interlocutor. Explain what you feel in a calm manner and let another person explain, what he/ she meant by saying this and that. And vice versa. When you see another person distressed with the conversation you lead, let her/ him explain what they feel and make yourself clear. The main thing here is to hold back anger and negative emotions. Also, it is highly important to respect the person you are talking to.
Getting help is crucial when you get stuck with the conversation and cannot find the solution. Sometimes no matter what you do and how hard you try to explain yourself, the other person simply cannot get it. So, inviting someone to join your conversation and help you to find a way out might be a good decision.
Offering help is a strategy of a high risk. You should be really helpful in solving the conflict, not willing to show you are the smartest and the wisest person. It is vital, that you stay respectful, calm and join in when it is really needed, or wait till you are invited.