Peace that surpasses all understanding to me involves being silent and waiting on God. I know that when I snap back, get defensive, or judge I do not have peace. In any conflict with another person, all it takes is one thought: he/she really does love me, I'm sure I'll learn from this, maybe they intended to help me with that, etc. Jesus can do a lot with a positive thought...just one thought.
I find that I have been finding peace now in times that I would be grieved in the past. God has really been revealing His heart to me. Today I opened up Lamentations - a book I had only read once when I read the Bible the whole way through. I turned to Lamentations and it was just what I needed. I think peace that surpasses all understanding also comes from clarity about what God can do with our hearts and with our situations, no matter what we feel at the time.
Confession, repentence, and purity. I have found these things to lead to peace that surpasses all understanding. Confession humbles me and allows me to realize I need Christ's love. Repentence allows me to give myself over to God in surrender and turn away from my currently focused on sin (pride, judgement, anger, etc). Purity helps me to realize that everything will be okay because God delights in me and I delight in Him. Pride, judgement, anger, lust, idolotry is blocked out by the light of my savior and love for me. I can be fine-tuned and grow from my mistakes - which brings glory to God.