Agree to Disagree
Effective conflict resolution is a trait that many successful people have taken great pains to learn and practice. It is going to be very rare that everyone you work with or go to school with agrees with everything you say or think. Instead of getting upset and refusing to work with those whom disagree, remain calm and learn new ideas from the situation. Here are ways to get the most from any conflicting situation.
Keep it objective.
Do not make this disagreement a personal attack. Remember, you are most likely upset with the situation or the idea and not the person.
Be open to new points of view.
Do not immediately put down an idea or opinion simply because you disagree with it. Instead of lashing out and screaming "That's the dumbest thing I have ever heard!" say something like "I don't quite understand or agree with that idea, and here is why I feel this way". Doing this builds a safe channel for mature, adult conversation. Never act sarcastic, rude, or disrespectful towards others in an argument.
Utilize "I" statements.
Talk about how you feel by using the word "I" instead of using the word "you". So, instead of saying "You always are annoying!" say "I feel annoyed when you don't listen to me."
Be a good listener.
Really actually listen to what is being said. There is a difference between listening and hearing. When you hear what is being said you are still probably thinking about why you disagree or what you plan on saying next. Instead, keep your mind blank and try to listen to everything this person is saying. Then repeat back what was said and show the other person you really are hearing them out and are trying your best to understand their point of view.
If you can remain impartial and calm and not let your emotions get out of hand, you will be much less likely to sling character accusations and make brash statements you will regret later. Rather, you will be much more likely to learn something new or to get something good for both parties.
The key to successful conflict resolution is to build safety and trust. By following these tips when you are in an argument, you be much more likely to emerge better off with an increased level of respect for the other party. This advice works once you are in one of these situations, however common courtesy and consideration towards another party long before a disagreement will go a long ways towards successful resolution.