Conflict resolution is a soft skill that needs to be taught at every organization. When a group of people are put together and asked to work with each other, it is laughable if we do not expect any sort of conflict to arise.
Imagine a box where different sets of opinions and different sets of personalities are kept together and are asked to figure out the solution for a problem. What you say may not necessarily be another person's opinion. And how you handle a conflict may be different from how the other person handles it. So how do you come to a conclusion? There are a few common ways in which issues can be resolved.
Usually to avoid conflict from a person who refuses to see reason, it is better to oblige and give in to them. This way you do get to avoid a conflict but it builds up a resentment towards the other person that grows the more you work with them. Although this is better in the case of a dominating person, doing this frequently with everyone will make you unhappy personally. So make sure that you do not get used because of your accommodating nature. It is important to maintain the balance.
2. Coming up with a win-win solution
If the person you are conflicting with is willing to see reason, it is easy to come up with a solution that benefits all. This is the best method of conflict resolution because it leaves both parties happy with each other and no growing resentment. This also means that the next time you have to work together, you know it's going to be a two-way street which means you can work smoothly with each other. Always try this approach first before looking at other approaches.
It is not always completely possible to satisfy both people in a conflict. While coming up with a win-win solution sounds great, it is not easy to arrive at it. So, the next best thing is compromise. Discuss and come up with a solution that has some sacrifices towards your end and some towards the other person. You may not resolve the conflict feeling completely satisfied but at least you will have reached a conclusion and you can move forward with the solution. This is the approach that is usually taken many times for smooth conflict resolution.