"In your anger do not sin": Do not let the sun go down while you are still angry,
The biggest thing that I would like to point out here is that this verse does not say that all anger is sin. You can get angry, yet not sin. This is important. There are many who battle anger by trying to never get angry. The key is to determine what we do with the anger, we can get angry, but not sin.
To tackle sinful anger, it simply cannot be done in one short blog post, but let me try to outline the path of change. The Put Off is fairly simple, we need to put off sinful anger. It says it right there, In your anger... don't sin. The Put On is a little more hidden here, but I believe that it is still here, in the next part of the verse. To "not let the sun go down" you are going to have to deal with the problem. Jay Adams, in a booklet on anger, says that anger is energy to solve problems, and I believe that there is a lot of truth to that. We need to deal with the issue, today if possible.
Just a couple of other thoughts: Dealing with anger doesn't always mean that you are to go to the person. Many times it does mean that, in fact on some issues, we are commanded to go to the person. Consider Matthew 18:15-20. Using wisdom and discernment, there are some times that it is good to deal with it within yourself. In other words, sometimes the offense is better to overlook, consider Proverbs 19:11.
Don't let the sun go down again until you have dealt with your anger.