Remember the objective. You are trying to find a resolution. That means you must be open to gaining new information. How? Separate the person from the problem. You cannot get a new outcome (resolution) with an old perspective.
Entertain the thought that the other person will communicate something of value. This allows you to be open-minded.
See the benefits of the compromise. Does the compromise free you from further obligation? Does it save your reputation? Does it give you more time to pursue your personal interests?
Operate from a non-emotional place. Communication is a two-way street, and you can leave a conversation whenever you want to. That means there is no need for name-calling or emotional escalation. Both people should agree to remain civil and focus on the issue, or you can take a break until you calm down.
Listen patiently and feel secure in understanding that listening does not mean that you agree. It allows gain information and allows the other person to feel heard which may improve the chance that they will listen to you.
Voice your concerns, perspectives, and preferences when it is your turn to speak. That is the only way to ensure that your interests are heard and included in the resolution.
Evolve. Conflict creates the opportunity for growth. Use this opportunity to learn more about yourself, the things that trigger you, the way you communicate, and how you can improve yourself going forward.