Forgiveness is the way of non-attachment. If you do not attach to your ideas, you will have no need for forgiveness. You will just forgive things as they occur. That may be an ideal way to be, but it is not where most of us are. We tend to hang on to our ideas of right and wrong and justice. When somebody treats us badly we stew. We tell our friends about what this person did to us. We get confirmation that we were wronged. We collect allies in our anger. This may make our initial wound hurt less, but it spreads pain.
Even more than the pain that others impose on us, we carry around a lot of pain we have imposed on ourselves. This pain often comes in the form of guilt and self reproach. Guilt is the more subtle of these forms as it can be generalized or felt without a discernible cause. This pain we impose on ourselves is harder to shake because we were the judge and jury that arrived at the verdict and imposed the sentence.
This is where forgiveness is helpful. Forgiveness is simple. To forgive yourself, all you have to do is connect with that part of yourself that feels like you meant well, recognize that you may have made a mistake, and feel the love.
To forgive other people, the Buddhist idea of ignorance is helpful. Although it is harder to imagine that you are ignorant, it is easy to imagine that others are, especially when they are hurting you. To forgive others, acknowledge that they are acting out of ignorance and find some love for their suffering souls.
If we practice forgiveness regularly, we will not become so attached to our problems, because we will see them coming and going so frequently. As we get good at connecting with the love that we feel for ourselves and our enemies, that love will flow through us and heal the world.