I was asked by a questioner, "How do I get over anger with someone?" My answer took me much deeper than I expected.
Part 1: A positive vision
This is a complex journey, and the 2 things that would have helped me the most would be distinguishing between feelings of resentment and genuine bitterness (they're not the same thing) as well as understanding that such feelings are not just a choice. Feelings definitely include choices, but you can't control feelings merely by wanting to be righteous, praying, reading the Bible, and choosing your attitude. Such spiritual disciplines are not sufficient without a vision outside ourselves of what can be better. When we are motivated by fear, the bad characteristics we're trying to remove don't simply go away, no matter how much we try to arrange our life. But when we are inspired by a vision of something better, like Jesus Christ's nonviolent response to His persecutors that led to His ultimate victory, that helps a lot. Feelings of resentment have a similar role as physical pain, a warning that something wrong is being done to you. Being upset with "a person" feels very much like being upset about "what the person did," but if you focus on the fact that the person's action was wrong, you blame sin, instead of dehumanizing the person who was made in God's image (likeness). Genuine bitterness is an active power which seeks to put others down in various ways when they threaten your sense of control. Bitterness, unlike resentment, is more of an engrained attitude. Regardless of whether the originating feeling is a surface emotion or a deep attitude, anger needs to be directed in healthy ways like praying about the pain you went through or discovering the best action to take to minimize further pain. Most importantly, don't define yourself by the pain; this is not as simple as just choosing an attitude or repeating a verse in your thoughts over and over. You have to find something about God which seems better than your current situation. Do repeat verses, but realize they are meaningful not as a superstitious mantra, but because they are within the context of God's great story of redemption, the Gospel, and Jesus' example has to be central in your healing from anger struggles.
At different times, I've been inspired by the narrative of Christ triumphing in His resurrection because of His righteousness; at other times by the realization that there will be ultimate justice for how we've endured with good character, but no peace for unkind people who seem circumstantially happier and don't seem to suffer like we do. However, this desire for others' punishment is not very satisfying, because justice that involves wrath and irreversible punishment does nothing except deter it from happening in the future. Justice for the Nazi war criminals means "Never again" accepting this kind of horror, but can't reverse the horrible pain of the past, and there's really no healing for those family members except if they knew their dead loved ones had peace with God and eternal life. Justice can't fix the past, but can only prevent a worse future. We have to remember that our priority as Christians is to create a better future, and that the only reason we can even see what's better is because of Christ opening our eyes.
Part 2: A desire for reconciliation
Relationships are very hard to mend. God wants reconciliation and is willing to forgive anyone whose heart wants it. Sin keeps people from wanting reconciliation with others and makes us think of justice as something we are owed, when it is actually something God chooses to mete out — or not. It is amazing that He would have forgiven even Judas Iscariot if he had wanted it! The basic difference between Judas and Peter was that Peter was trying to be a good person and Judas didn't care. Peter betrayed Christ just as much as Judas, and still had a lot of struggles after Christ's resurrection with accepting God's grace in John 21 and the Book of Acts. Peter's legalism also made him resistant to evangelizing Gentiles, like Jonah in the Old Testament who wanted God to punish those heathen Ninevites. Christianity is so radical because it openly admits that it's better to just forgive and wipe away the sin than punish it — while concurrently putting equal pressure on the sinner to own up to the sin and repent, but through God's help instead of just by trying harder. No other belief system is so well-rounded in its concepts of justice and freedom, including the punitive Old Testament Mosaic Law which didn't allow for forgiveness unless you did something extra to earn it. The early Old Testament's view of sacrifices was that they would satisfy God, but Job, some psalmists, and the prophets recognized that sacrifices just demonstrate that the wages of sin is death and that everything we have comes from God; we can't buy His favor, just express our own appreciative and repentant attitude. Then Jesus revolutionized this concept further by showing how much He longs for our fellowship instead of our fear of His anger. Then he made Himself both the sacrifice and the recipient of the blessings. Jesus' example demonstrated that in the long run, we are happiest when we give.
This extends to our giving of mercy. When justice involves only vengeance, and God's mercy is understood just as a lessening of the punitive punishment, it's not satisfying to anyone. Contrary to punitive punishment, when punishment is intended to help you grow, it's productive discipline. The reason human justice can't be very lenient very often with criminals is because we can't know whether their hearts have truly changed, while God, who knows if a heart is changed because He changed it, is able to totally forgive and restore people. Still, the situation gets messy when there are relationships with other people involved; sometimes the other people aren't willing to forgive, and sometimes other damage (like a divorce and remarriage or a death from drunk driving or murder) has been irreversibly done. We have a linear existence and live in a world based on consequences. Some things can't be healed except through a miracle, but God's miracles are rare compared to how often things go wrong.
Whoever you're angry with may not want to reconcile with you, and if you were close to that person, you probably are tempted to invest yourself less in future relationships. God made us keenly aware of our struggles and desperate for a solution, but He didn't make it hard for us to find the solution. Rather, it is our sin nature which does that. First, you need to evaluate yourself as to whether you want to punish the other person. If you feel a desire to punish the other person, what are the reasons? Do you think it's just a matter of civic justice or personal hatred? When you think about the other person, what goes through your head? Do you actively wish harm upon him? Have you come to understand why that relationship deteriorated and whether you had a part in it? The attitudinal choice to forgive does not automatically remove the feelings of helplessness and anger, but it is the foundation, because you're saying "I give up my right to punish you" (as I heard once on Christian radio — the perfect definition of forgiveness). Reconciliation is impossible without agreement from the person who hurt you, but healing is not. God brings healing if you take your struggles to God in prayer, continue to go through the Bible, and pursue something healthy that really makes you feel good. I believe God can help anyone find hope for the future if they let Him.
Part 3: A change of outlook
Situations are very hard when you can still communicate with the person you're angry with but aren't able to have that emotional transparency because there's a divisive issue or unresolved pain which they (or you?) won't be humble about. Even if you understand why the other person (or you) acted wrongly, it doesn't allow reconciliation if the other person is too defensive to open up and work through the issues. The positive way the Apostle Paul looked at his times of greatest struggle is that Jesus went through those kinds of struggles and triumphed. But it's not necessarily going to make the struggle easier just to think and focus differently. It's going to take time, and sometimes an unbiased mediator, to help you move on.
For me, feelings of resentment pass within a day after I've been hurt, because it's just my body's way of processing the pain, but if I had become poisoned by hate, it would've made me self-destructive. Some temperaments handle anger differently. You might internalize it more, like I naturally do, or externalize it more, and those who externalize it seem scarier. People who are depressed are often internalizing either anger or fear. For me, it was fear rather than anger which fueled depression in the past. After God helped me understand the causes of certain family members' lack of compassion toward me, which were rooted in their own upbringings, it helped me not feel the confusion about "Why" very much anymore, but I continued to feel fearful because I didn't see a path to my own well-being away from them. Since then, I have come to realize that even if I was free from them, I would still eventually have to deal with other difficult people, even if not necessarily as much. We all have our crosses to bear.
The thing that has helped me not resent God for it is that I see that even Jesus couldn't change His situation, but still won in the end. He couldn't redeem the world without dying, so you could say even God has limits on what He can and can't do. I break from Calvinism in that I think we have an equal part in choosing whether to be saved; I think He can't force someone who's unwilling to believe in Him. Individuality and God's provision for people who believe are the most amazing mysteries I know of. How does God give someone individuality and yet also work through them or fight against them? What was so satisfying to Him about giving mankind freedom to choose good and evil when He knew He'd have to kill Himself and temporarily fracture the relationship with Himself ("My God, my God, why have You forsaken Me?") to redeem us? Those kinds of things will help you if you think about them, because they'll give you hope about a better ending to the story and get you focused more on God's love.