Anger is a particular set of physical sensations that arise in response to certain thoughts. The best way I’ve found to disarm anger is to break the link between the thoughts and the physical sensations.
You do this by turning your attention away from the thoughts about the situation causing the anger and focusing the attention on the physical sensations of anger. Do this with a spirit of open investigation, like a scientist doing a detailed and objective study of what an angry body feels like. Notice that there’s nothing particularly negative about the sensations; it’s just the body’s collection of arousal responses. Feel them as completely as you can, not pushing them away (since they’re not, in themselves, negative).
Even though you’re not actively trying to get rid of the sensations, they will gradually fade because your attention is no longer occupied with the thoughts of the situation you’re mad about. Continue to watch the sensations as they recede and go away.
Going back to the thoughts after this may cause the sensations to come back, but they usually have less leverage on you. Repeat the process.
You’ll still need to address the conflict that brought on the anger, but you can reason much more clearly about the situation once the sensations aren’t infusing all of that aroused energy into the picture.