Forgiveness is a strange concept. Though it is clear in the scriptures and the Catechism of Catholic Church, understanding it and following it is difficult, but not impossible.
I have understood only this one thing, whenever I need to forgive someone or myself, I only need to look at the Crucifix.
Another thing has helped me. Whenever I am offended or hurt, I think about the times I have hurt, wounded, offended others with whom I interact daily at home or work or strangers. I remember the times I was acidic, sharp, demanding, unloving, judgemental, selfish, or purely evil in my thoughts or intentions. That is enough for me to discover, how great punishment I deserve for my failings and sins and I continue to look at the Crucifix and then can start loving and praying for the person that wounded me.
I am in need of redemption on a daily basis, even when my Savior died and paid the price for me once for all. But I need to claim it daily.
Lord Jesus, grant us the clear understanding of our own deeds, thoughts, words, and omissions, so that we may become gentle and just like You. Teach us to love like You do Lord, so that we may love, because when we love, we forgive. Amen.