Conflict is hard -- really hard. That is why most people try and avoid it, especially at work. But ignoring it is one of the worse things you can do and can, ultimately, do irrevocable damage to your career. Here is what I've found works really well at overcoming, and conquering, the fear of conflict.
Know How to Present the Problem
One of the things that I always consider is how I can present the problem without hurting the other person's feelings. I think in many cases what happens is we tend to take feedback, or confronting a problem, very personally. It's very important to be sensitive to how you approach that person to make sure that they understand that this isn't personal, this is about something that's going on at work, and it has no reflection on how you feel about them or whether you think that they are a good person.
Don't Wait
I think one of the most important steps in the strategy is not necessarily how to do it, but to do it quickly. Don't wait. The minute you start to see a problem or the minute you start to see the conflict coming up is when you should address it. By leaving it, or not addressing it, or letting it alone, many times it makes the situation worse. So, the best piece of advice is, the minute you see it, deal with it. Don't wait. That way, it will be less contentious, there will be less emotion, and, often, you can defuse the situation very quickly, making for a far better working relationship.
Escalate Smartly
I think one of the things many people forget about is that they have supporters and people they should be able to turn to inside the organization for feedback and advice. My best advice is always to talk with HR first. They are your advocate and you should be able to feel that you can go to them with a problem or for advice, and sometimes they can help to broker a conversation. If you're not comfortable or don't want to get HR involved, one of the things I've always recommended is to take a step back and think about how you want to discuss the problem with your superior. Ask for some time, get on their calendar, and talk about the situation using words like "I," "How can we solve the problem," "This is how I felt," and "This is how it made me feel."
Sometimes, people aren't aware of their behavior or language. Even talking about it by saying "This is how I saw it" or "This is how I perceived it" helps to bring awareness to the situation. If you can't seem to make any headway with your superior, then you really do need to think about whether or not you want to escalate. Escalation doesn't mean that you're rocking the boat; escalation means that you're trying to solve a problem. In many cases, if your superior is not responsive to you, there are probably other problematic relationships inside of your team, and you should think about how to work with HR or an advocate -- maybe a person who's on equal footing with your superior -- to help you solve that problem.
Share with the community some things that have worked for you when you have had to deal with conflict at work.