It depends on who the person I'm having a conflict with is and my relationship with them. Depending on that my style can be rather different. With my husband I don't avoid conflict and always like to bring things out in the open and work through things. With other people I generally avoid conflict unless the issue is too important to ignore.
Generally though I try to focus on the point of the conflict and not get side-tracked. I also try not to give in to emotional temptations that would complicate the issue or make it worse. I like to talk about things calmly. Expressing true emotions is ok but I don't like over-the-top drama.
A lot of this depends on actually what you mean by conflict.
If I'm having a conflict with another person (where he/she is angry at me), it all depends on the reasoning behind the conflict. If I believe that I am right, then I will defend myself by saying why I am right. If the person doesn't let up by arguing his/her case with no logic behind it, I will just tend to avoid him/her because it's no use dealing with such people.
Usually I'm very quick to forgive, but I don't make it openly clear (like I won't say 'I forgive you', but in my mind I have forgiven them, even though I don't forget). I will avoid unnecessary personal conflict (I'm not the type who goes around looking for a fight - that's just idiotic).
When I see people in conflict, my first thoughts are that they are probably overreacting, and now they aren't thinking as clearly as they would normally--when they could've straightened things out. So I leave, and let them handle it.
When it happens to me...I try to keep that in mind, not to overreact, and to keep language polite to show good intent. It's harder to do, though, especially when someone is just trying to egg me on and get a reaction from me (they may get it ). One thing I like to do is turn away when the person isn't worth it, in that way making it known that I'm not going to bother arguing with them.
SJs love conflict. No, I'm teasing.
(ESTJ) My father loves it for some reason,
he thrives off it. Not me.
"Fools who wear their hearts proudly on their sleeves,
who cannot control their emotions, who wallow in sad
memories and allow themselves to be provoked this
easily -- weak people, in other words -- they stand no chance."