With the right attitude and a clear understanding of the situation, conflicts tend to dissipate without any invested effort.
Even if you can avoid conflict on a personal level, collectively some solutions can be preferable to others. To solve conflict the optimal way, there is no alternative but communication, communication, and communication.
Through communication, conflict solving works by aligning the goals and desires of everybody involved. Often we find that the goal we focused on is a bit shallow, and there is a deeper goal behind it. By going deep enough and being understanding of others, conflicting personal goals merge into a single collective goal.
If there is a clear single goal and if everybody is willing to contribute, getting from point A to point B is a snap - and conflict is solved.