When faced with a conflict there are three skills that are key:

Get your emotions under your conscious control
Behave differently from how you feel.
Look beyond the present moment... look into the future and decide your best outcome and what you really want. Then come back to the present and initiate the actions that will get you there.
To utilize these three skills - you need to practice on the small and minor irritations before you deal with the big conflicts.
Through all of the above... you must understand and buy into the concept that you must focus on you - not on the other person... not on the 'why' of the conflict - not on who is right and who is wrong... You must first focus on getting you under controllll and understanding what YOU want and what is the best outcome for YOU. After that - you can then focus on Win-Win and other conflict resolution strategies!

Get your emotions nder your control