Conflicts happen all the time in a working environment. This is why it is important to solve them constructively. Such that both parties can continue working together. Andrew Grove (Intel's CEO) has developed a simple algorithm for solving conflicts. It consists of 5 steps:
The main goal of this step is to identify a problem. The real problem rests with people, money or time. If you can live with that, maybe it isn't worth solving. Try to ask yourself what happens if I do nothing about it?
Once you identified the problem it's time to think about what you want to achieve. What is the goal of the upcoming negotiation? What your interlocutor should change in its behaviour?
Understanding problem and goals won't help you solve the case until you plan your approach. Take into account what your coworker wants, put yourself in its shoes. Find the best arguments to convince your teammate. The best arguments based on believes and goals of your interlocutor. Don't fix people, fix the problem.
Now it's your turn to present the problem to a teammate. Don't throw all arguments at once, use active listening. Present your arguments from previous step one by one - argument, pause, argument, pause and etc. You should reach an agreement regarding the problem on this step. If you can't convince your coworker on the problem presented - stop and take some time to think more on the problem, don't push.
It works best when the solution is proposed by an executor. Help your teammate find a solution. Review alternative solutions and choose one. Define who, what and when. You can use the RACI matrix for answering these questions. Write a follow-up email.
This is the last step and many people forget about it, but you shouldn't. It's important to check that solution works for both parties. Also, use this step to appreciate the efforts of your teammate.