Now, I can't tell you that you should "just let it go" or that I have some miracle cure that will instantly make you understand how to set your anger at someone free, because I don't. Truthfully, I still harbor angry thoughts about a few people and situations in my life--but understanding this anger and learning how to process it is a great step in beginning to move on from it.
In my own experiences, when someone is angry they're usually not simply angry, there are underlying feelings that are emerging through the anger like hurt, jealousy, or betrayal. Sometimes even love. Harboring resentment over something definitely means you still care about it, even if you don't want to admit that. The first step in this long process would be understanding what you're feeling and why you're feeling it.
I'll use a very personal example. I am so angry at my stepmother that I feel like I could punch through a wall when I think about her. She's poisonous, she is unstable, I don't trust her, and I worry about her effect on my father. I am so angry I could spit. Or cry. She has caused so many problems that I really don't want her in my life at all. This being said, I won't let myself detach completely because of my father and, to a degree, my brothers. I love them and I want to see them and, unfortunately, it means seeing her as well. (Don't get me wrong, if it ever reaches my breaking point, I'll have to stop seeing all of them because of her but right now I love them too much to let her ruin it.)
I spent a while living somewhere very near to hate when I thought about her until I realized her presence in my mind was crippling me so much I couldn't function. I also realized, in addition to my anger, I am feeling hurt because of the way she treated me, I am betrayed, hurt, saddened, and fucking PISSED at the way she treats my dad, and I'm angry that I can't do anything about the situation. Understanding why I'm feeling this way is the first step in letting anger go.
(the presence of these gifs helps neutralize my anger as I write)
Now, I can't claim that I'm not angry at her anymore. Honestly I still don't want to be around her at all and I'm not anywhere close to forgiving her, but now that I understand why I'm angry I can begin working on not worrying about the anger I'm feeling, putting it out of my mind and putting myself at ease.
Moving on from the personal and into the more general, it's a very difficult thing, to release the anger you've harbored for a long time. But understanding why you're feeling what you're feeling, maybe even discussing it with someone you trust, is a great place to start. I'm not an advocate for the "forgive & love everyone" life method, mostly because I'm not sure I can forgive certain people. (I'm pretty sure I'll be 80 years old and still feel the anger flare up when I think about my stepmother.) But I am a major advocate of the understanding & reasoning approach to life and anger. Talking it out can really help you release the bottled up feelings, and if you don't have anyone close you can turn to--you could try a therapist, they're quite beneficial, you could write a letter to Dear Abby, and, there's always little ol' un-solicited-advice-giver me.
And here's some more unsolicited advice:
Don't listen to naysayers when they tell you that what you're upset about is inconsequential or not important.
Don't feel bad if you can't release the anger at all
Do try to understand why you're upset--and connect with the feelings you're feeling other than just the anger
Do let it out! Scream, yell, cry, throw a pillow, hit the pillow, shred the pillow--anything you have to do to let the feelings out
Have you had to deal with anger at someone? Were you able to forgive them/the situation? If you haven't forgiven them, do you think you are able to? What are some of your methods of dealing and understanding your feelings? As always, feel free to comment or talk to me through any of my varying methods.