I tend to lose my patience really quick.
When there's conflict that doesn't involve me/involves me indirectly, I avoid it. Just stay quiet or go away. When the conflict involves me, I try, first, to give some ideas to solve the problem, if the person/s in question don't back down, I may add a snarky comment. If that doesn't work (which never does), I may try to find allies and find a bigger way to solve the problem (like explaining the problem to someone with more power, always making a sad dog's face). If there are no allies, I'll grab the person who has the problem, sith them on a chair and knock them off the pedestal and work out a solution.
Now, when there's someone insulting/offending me, I set things straight from the beginning: you're not respectful with me, I'm not going to be that way with you. I won't let you talk and make sure you don't ant to keep talking afterwards.
Best example is from a month ago, when this hysterical girl entered the classroom I was in to curse at me because I had never been to a subject (where attendance didn't count) and I had the best grade because the portfolio of the class I presented was really good. According to her I had paid the professors and made other people do my drawings and such. She was mental. I turned back and said: "look, I spent 2 years learning to draw, I practiced everyday, made people who know how to draw correct me until I got good. Even if I was a genius and I hadn't needed any practice, you could have compensated that by sitting your ass on a chair and doing what you had to do; you could have reached for help; idea that never occured to you, because you preferred to come here to humilliate yourself in front of a group of people. Now, as you can see, I'm in another class, professors are correcting our works. If you're done with your hysterical speech, you can leave. The door is behind you." Then I turned back and continued doing my stuff. The girl gave me a death stare and went away.
I try to be pacific and find the most neutral way to solve problems, but if someone insults me, my friends or my opinions, I'm speaking up.