It always depends on the situation. If the person has wronged you publicly I find that the most satsifying thing to do is vent to someone completely unrelated, and act like the most dignified person in the world when you're in public.
The compliments you receive for your behaviour help to calm you and make you rise above it.
If the anger is really hurt, then usually it doesn't fully go until the pain goes.
It may not seem so at the time, but all life experiences are ones from which we learn; look to the positive to find the lesson. Every cloud and all that...
The wrong you experienced is a value you don't share; be strengthened in the knowledge and live by your values.
When someone has wronged me intentionally then I make myself not be angry, hurt or upset. If distress was their intent then I know that it didn't work and feel so superior!
If the offence is accidental then sometimes a quiet word along the lines of "I know you didn't intend to ... but I just wanted you to know that the outcome of your words/actions was that I was really hurt". I taught my (6!) kids this one - despite your intent, the outcome is what is important, so think before you speak/act.
In this situation, it's good to remember that we're not perfect. If our friends irritate us, or someone has offended us we'll probably do the same to them from time to time. Just think, 'If it was the other way around, how would I want things to turn out?' With a little love, mildness and humility you can let go of any resentment. And forgiveness helps too.
Life's too short to hold a grudge. Talk to the person, explain tactfully and calmy how you feel and see what they say. If the apologise so much the better, forgive and ACTUALLY forget.
If they don't, well then sometimes you have to leave it behind for your own sake.