To let go of anger and truly forgive is a long process at first. I think you get better at it over time.
I know what is helping me is to look at people, including myself, like I would if I were a higher being. Take all the personality out, and just see them for what they are - damaged people. We all hurt, we all make mistakes, we all long for companionship, and someone to understand us.
When I take away the specific deed that has caused me pain, and look at the person who committed the deed through the lens of: "Wow. This person is really, truly broken. I wonder what awful things have happened in his/her life to have caused them to become so awful?" - I see them distilled to something far more pure. I hope that makes sense. I'm looking away from the crime and into the damaged parts of someone.
I feel so much compassion when I realize how broken they are. No person who isn't damaged would do the kinds of things we're being tasked with forgiveness for. I can feel empathy and sorrow on their behalf.
When I get to that point, I'm able to forgive, based almost completely on compassion for another wounded soul. I give it up to the universe, so to speak, because I don't want to carry the burden of being hurt by their actions any longer. I also realize their actions weren't entirely personal. They are the reactions of someone very, very damaged.
So, it's easy to forgive when I'm in tears for another's pain and suffering. Sometimes I find I'm not quite there yet, and I'll choose to forgive, to send it away from myself, again and again, until I've released it all.
My spirit is lighter and happier not carrying around grudges and anger based on another's actions. Who knows what damaged place in their psyche the action came from anyways? It's on them, and not on me - I've released it.
And it hits me as I'm typing this...releasing is really what forgiveness is about. It's letting go of the pain.