It's challenging facing conflict when you are an empath, especially when you are unexperienced. This is due to the fact that you could be picking up the other persons anger, and having it mix with your own, which doesn't help.
I'd say I deal with conflict fairly well. I don't allow another persons anger to get to me, while at the same time saying calm about the situation.
I would recommend practicing breathing techniques, and if you do find yourself in a situation where you are faced with conflict, I would advise you mentally take a step back and evaluate the situation, before going calmly about resolving it. A trick I like to use is to imagine blue energy swirling around me in a bubble, where all noises sound distant. It gives me a kind of calm-watery feeling.
Let me know if that helps!