Workplace conflict is a natural part of employment and the use and obtainment of resources. People come into the workplace with all types of needs and expectations. When these needs and expectations are not in alignment with what others want there could be conflict. Resolving and understanding conflict is important for resolution and moving past potential problems.
The first thing to do is sit down and realize what is really important to you. Many people are unreasonable and unwilling to compromise. While that strategy works sometimes it can also backfire in poor relationships and getting less than you want. If you understand what is important you are likely to avoid the pitched battles.
Come prepared. Expect differences of opinions and what your argument is for those positions. Don't always try to win but simply to understand what those arguments are and any reasonable solutions. If you start with a high position expect to be countered. Know where your line is and why you should or should not accept a different outcome.
With most arguments there is the possibility that things will get heating and become personal. Don't allow it. As soon as someone becomes personal state your position and back away. Expect and demand respect or you will not engage further in the debate. You must also give that respect. Be civil and take your time to think about all issues.