Here's what I came up with:
Determine what you need to gain from the conflict.
We often have conflict because our needs are not being met or there's some sort of power struggle. Are you having conflict because you're feelings were hurt and you need an apology? Did someone take an important responsibility away and you need to find something new to make yourself feel useful again? Are you just butting heads with someone and you need to find a way to work together anyway?
o What you hope to gain out of this conflict
o What the ideal outcome of the conflict is and whether it is realistic
o What your plans are for getting what you need
Now put yourself in their shoes.
I know this seems awfully difficult and perhaps even unnecessary. Alas, it is very necessary and important in order for you to get anywhere in resolution.
You want this person to see your side. You want them to understand what your needs are in this, so you can feel understood and the problem can feel resolved. Then you can move on.
Well so does she (or he). She wants you to understand what her needs are in this, so the problem can be resolved. Then she can move on.
Try working together.
The first step here is to recognize part of the problem is your fault. You are half the conflict. It "takes two to tango" so to speak. Blaming the other person will not resolve anything, but understanding your role in the problem at hand will.
Approach collaboration with calmness and confidence. Getting emotional will not resolve anything. Remain calm and collected, choose your words carefully, and speak with confidence. Remember, there are two goals: to help the other person see your side, and to understand his or hers.
Finally, avoid battle phrases, or things like, "you always," "you never" and "you make me feel..." These phrases increase the other's defensiveness, and can result in emotions flying off the handle. No one likes to be accused of anything, let alone making you feel anything. You are in charge of your own emotions, so no one makes you anything except you.
Essentially, stick to the facts, and focus on the real problems and issues.
What are you willing to compromise on in order to resolve the conflict? What is the other party willing to compromise on? Can a compromise even be reached?
You won't know unless you ask. So man up, open your mind and your heart, and approach the person you are in conflict with. Is it possible you can come to an agreement?
First and foremost, continue to do your work, and do it well. Do not get distracted by your conflict, or swept away in gossip or emotions. It's easy to do this because if other's know about your conflict they will ask you about it. Everyone loves dirt. But, talking to co-workers about your issues doesn't make you look good should it come around to the boss that you were blabbing about it.
If you must, go to Human Resources. But make as much attempt as you can to resolve the problem on your own first. Take notes of these encounters and hang on to any emails, notes, memos or other items you collect in relation to the conflict. Then, if you do need to go to HR, you have a trail of your communication with the other party. If the other party is particularly mean during all this, or bullying you, then this documentation becomes even more necessary.
If you keep your cool, and attempt to show the other person an agreement is desired, your conflict should resolve itself.