No, this isn't written from the perspective of, "A guide for complete beginners." It's okay to laugh.
1) Talk loudly, and interrupt frequently. It's important to work out your problems in the height of your emotional distress. Best case scenario, write an angry letter, and DO send it.
2) Exaggerate your case. If necessary, bring your children into the conversation, and use the word "devastated," as in, "My children are devastated that you think I have a bad attitude."
3) If you can't avoid the conflict entirely, try to resolve your conflict via email. About 90% of communication is nonverbal, so bank on the 10% to get your points across clearly. This way, you can say everything you need to say without being interrupted, and the other person just has to take it. Like a bullet.
4) If you are the avoidant type, become resentful that you are even having the conflict in the first place. Use phrases like, "In my 15 years of being in X position or at Y job, I've never had such difficulty!" The problem, after all, is them. It's not you. You are too mature, wise, and flawless to have any character defects after this long. I mean, you get along with everyone else so well, so surely the problem is with them. Especially if you are Christian, Jesus has been "working on you" for a long, long time, and has ironed out your most noticeable imperfections. Consider Him on your side. Religious fodder (whether implicit or explicit) is especially welcome in the world of interpersonal conflict.
5) Since your intentions were obviously great, please, by all means, do NOT -- I repeat, do NOT -- consider or acknowledge the other person's feelings! Bad things will happen to you if you do. Well-intentioned people rarely make mistakes, and when they do, your convo buddy should be expected to overlook them because, hey, you didn't mean to sound like a priggish jerkweasel. You didn't intend it, so therefore it isn't true.
Hope this helps!