This is a difficult topic to write about as conflict always stirs up extremely intense emotions. As a former public school teacher, I had to sit through a number of classes/worshops which dealt with conflict resolution. I can only say that it is much easier on paper than it is in real life. One of the problems is when we are confronted by conflict, it triggers a "fight or flight response" because in some way, we feel threatened. The threat does not have to be physical in order to trigger a physical response. It can be psychological as well. Ask anyone who has experienced anxiety prior to taking an important exam and they will tell you about sweaty palms, feeling flushed, fluttering in their stomach and not being able to think straight.
Not being able to think straight. That's right. At the very moment when we need to keep our wits about us, our higher order thinking functions actually shut down and we want to either run or fight in order to make the conflict go away. We need to recognize this if we are going to deal with conflict effectively. If possible, we need to step back and breathe before proceeding with resolution.
As a Christian, this means that whenever possible I need to "be still" before God. When it comes to conflict, only God can see the situation perfectly without bias and when we are quiet before Him, He will help us to see things from His viewpoint rather than our own. It is not always possible but if the conflict is with a fellow believer, it is good if all parties do this. I have seen conflicts vanish immediately when people take the time to genuinely come together in prayer.
If resolution between yourself and another party seems to be going nowhere or you feel that your emotions are too intense, bringing in an impartial third party is often helpful. The key here is that they need to be impartial, they need to be a good listener so both parties feel like, well, like they are being heard and both parties need to agree to listen to and at least consider the words of the third party.
Finally, and this part may be somewhat controversial, we need to learn to walk away and shut the door. This last part can be extremely difficult for Christians as it seems to be unloving but is it? There is a difference between turning away from someone in anger and maliciousness and simply walking away from a toxic situation that is a breeding ground for destructive thoughts and behavior. Toxic relationships are just that. They are poisonous and if we cling to them, we are not doing anyone, including ourselves, any good.
There are times when we must walk away and perhaps even end the relationship. This is usually very painful and difficult because we want to rescue people but we need to remember that we can save no one. Only God can do that. We can continue to pray for them, we can even continue to love them but we must put up boundaries not just for our own good but for theirs as well. As we all know, there are consequences for our behavior and hopefully we learn something from them.
The one thing I do know is that is never a good idea to let conflict simmer on the back burner. We need to deal with it as quickly as possible lest it become a pressure cooker that explodes.
Finally, whenever possible, keep conflict between the involved parties. By that I mean, do not gossip about it. Quite frankly it is no one else's business unless someone is a mediator or genuinely needs to know about the conflict like a pastor, boss, counselor, etc.