Conflict resolution any advice?

You only have two realistic options,

1. Fry them up some bacon, and be nice.

2. Fry them up some bacon, then hit them with the pan while eating said bacon.

Strip down until you're wearing nothing but your birthday suit. I guarantee that the conflict will seem less than insignificant at that point.

Are you talking about a physical conflict or verbal; big difference!

*****PART 2 - CONTINUED from previous comment****

I also agreed with this part: "Resist saying your side of the story, because that will prompt the person to say THEIR side, which will cause you to state your reasoning again." But I wanted to add, also just LISTEN to the person when they say their side. This will help if/when you want to explain your side. This is a good tactic to try instead of "pretending that they're right." I could never even do that part because that would mean pretending you're wrong, which means deep down you're not opening your mind to the possibility you might actually be wrong, even if you turn out not to be. You might realize that part of it was a misunderstanding (it might even have been misheard). Just treat them with the same respect as you would appreciate be given to you. It may be difficult, but remind yourself this is a person who has value to you, otherwise you wouldn't care to try to convince them of your opposing POV. What I've found works for me recently is to take myself and my "intentions"/"knowledge" out of the equation while they are explaining, pretend the person is telling me something regarding their situation with someone else instead of me, and I am listening to what they say so I can give them the best advice on what to do. Conflicts escalate because the parties involved do not feel heard, understood or respected.

"Apologize (even if you still think they're wrong) and tell them that they're right." I also agree with this to some degree, but mostly because even if "your insides...burn with anger and pride," (great, and very accurate description) eventually you will most likely be sorry in some way, shape or form, and if it's with a loved one, you'll be sorry that something so stupid made you argue with/hurt/lose someone you love for so long, making you both miserable on your free time in the precious moments we all have in our lives that we're supposedly sharing with one another because we delight in making one another happy. So yes, "you ignore that," but not necessarily "Because you are the smarter, bigger person who had enough control to diffuse the situation," but more because whatever this conflict is about, it must be resolvable with something we can figure out with our brains, but we're often arguing with our emotions.

At a time when you are not having a conflict with the person, ask to speak to them about your conflict resolution solutions. Tell them you realized your method is not bringing about positive results as much as negativity and hurt feelings, which is never your goal, so you would like to work on this and would like their help. This will put them in a completely different frame of mind. Don't be surprised if their jaw drops. Continue by saying that you're not saying you're always right, or that they are, and you also realize that it's never all either party's fault, but that both/all have responsibility in conflict escalation, usually due to emotions getting in the way of communication of information or a point of view that is trying to be explained and understood. Let them know you want to do agree to something different now. This will indicate to them that you are serious about wanting to change this. Then tell them that next time you are in a conflict, as soon as you realize it (raised voices, interrupting, anger, faster breathing/heartbeat, that "familiar feeling" rising in your chest), you are going to say something like "5 minute walk" and then you will both agree to take a break from the conflict - both stop talking, period, one leaves briefly if possible, and then returns after emotions are calmed. This does not mean "admitting defeat" or anything of the sort - it's just a break. If the conflict continues, take another break. Remember why you care. Make sure to hug, if it's appropriate. Then do something nice for yourselves to remind yourselves of why you chose to be in each other's lives.

Hope this helps.

Eat humble pie even though you have nothing to be humble about.

Live to fight another day.

Best way to stop a conflict is to think of the situation from either an outside point of view, or the opposing persons point of view.
Resist saying your side of the story, because that will prompt the person to say THEIR side, which will cause you to state your reasoning again. You just pretend that they're right. Apologize (even if you still think they're wrong) and tell them that they're right. Mean while, your insides will burn with anger and pride, but you ignore that. Because you are the smarter, bigger person who had enough control to diffuse the situation.
Example of a situation diffusing statement; "You know, I thought about it, and you're right. I'm sorry, you're absolutely right." No sarcasm, just your best pure intentioned voice.
They probably ask you to clarify "So you agree with me? You're not just saying that?"
"Yes, I just didn't think of it that way until now. I totally agree with you."

Google nonviolent communication. I don't know much about it but it's worth a shot. Also use "I" statements whenever you can. Instead of saying, for example, "you make me feel like crap" try saying, "when you do or say such and such I feel like crap."

It might sound corny but the Serenity Prayer is a really good resource:
God grant me the serenity to accept the things I cannot change,
the courage to change the things I can,
and the wisdom to know the difference.

I'm powerless to change the volatile people so I choose to spend as little time with them as possible.

Try talking to them, explain your side of things and if that doesn't help, ask if there's anything bothering them. Just listening to each other works wonders.

LOL, this comment will be a two-or-more-parter since IIN said "my comment is too long" (story of my life). This, I believe, is definitely worth it, because of how much unnecessary sadness that can be avoided.

As I said in my reply to them, I think the solution offered by ccjigsaw is great for the most part, but part of it has problems that may develop. I used to and still often do have the same problem as the OP, but it's less and less since I tweaked this solution a little bit. I put in all the background on why it didn't work in that reply, but the solution I honed and have been using recently has been much more successful and productive, although it's much more difficult. I imagine over time it will get easier, though, and it is so much more gratifying, for everyone.

This solution of saying "you're right" when I didn't believe it just to escape the conflict didn't work well when it was with someone I cared about. In those cases I was too emotionally involved with them and, deep down, really wanted to have them understand me so we could put the conflict behind us. Instead, I was more critical of those who were closest to me, and less loving on the outside, and I refused to back down. I was stubborn, people walked on eggshells around me, and I lost many friends over time. People tried to get through to me sometimes, but it didn't sink in until years later.

When the time came that I realized I was alone, though I had no idea why (because I *knew* that *I* was a good person), I had to look at my own behavior as perhaps being at least part of what contributed to the negative outcome (hurt feelings, damaged or destroyed relationships). When I started taking myself out of the situation and looking at it from a completely objective POV/from the other person's perspective (making sure I was not adding in what I already "knew" I "meant" at the time, but just concentrating on how it appeared or how they may have taken it). When I did, I finally, finally realized how much I had been hurting people. It finally dawned on me that though I felt they should understand *me* or "know" me, so I didn't have to be as gentle and sweet to them (therefore I treated strangers with much more kindness than my closest friends and significant others), I really should have been considerate of the same from them, and with me knowing myself, I should have taken it easier on them because they were so patient and understanding with me. I also realized that I wasn't always right, and not only that, even when I was, it wasn't worth hurting, shaming, traumatizing or alienating the other person and damaging or destroying our relationship to prove my point. It made me very sad and I realized I had to change my own behavior if I wanted a different result. The worst part of these arguments is that I felt misunderstood and then when they would pull away or leave I would be deeply hurt mainly because I realized I had hurt them, and that was the last thing I ever wanted to do.

So I realized the truth of what ccjigsaw said so succinctly: "Best way to stop a conflict is to think of the situation from either an outside point of view, or the opposing persons point of view."

*****TO BE CONTINUED IN PART 2****

I think it depends on who started the said conflict; you or the other person.
If it was you, then take responsibility. May be a good idea to explain that you think it is getting out of hand, apologise and take yourself physically out of the conflict.
It was the other person who started it, then this can be hard. Some people love conflict and will do almost anything to start some conflict. Personally, I don't like to back down to these sort of people, apologise and walk away because that is what they want. In their eyes, they have won and are better than you. I hate feeding these sorts of people's ego. Assert your point in a nice, polite manner, do not raise your voice. If they raise their voice explain you think they are getting irrationally angry and out of hand, then leave. Walk away, be silent and don't turn back. Thus you have walked out the bigger person and proved they intentionally start conflict and are an asshole.

WAR

Knock your oppoenent out.

Aim straight, don't flail your arms about like a looney. Just clench your fist as tight as you can, and STRIKE your enemy so hard that they don't wake up for 6 weeks.

Conflict Resolved.