I don't think it matters too much "how" one observes anger, merely that one actually observe it as it happens, or at least after it happens -- most don't.
I could say some stuff, but it might not be relevant, because knowing what anger looks like without having observed it, it's kinda like explaining color to a blind man, you know?
But here: Anger arises only because we were angry in the past, and do not yet know how to deal with it. We get into a stressful situation (craving and aversion, where we can't get what we want or can't avoid what we want to avoid) which typically involves other humans. And instead of taking responsibility for our unskillful behavior or recognizing that others are ignorant (and that's OK because we're ignorant too), we become angry. It feels easier to blame others than to take responsibility, or to hate others instead of expressing compassion for their ignorance. This is why we feel, "I have a right to be angry, I deserve to be angry". And overcoming the anger, seeing through it, feels like an embarrassment, like you suddenly realize you've just been saying, "I have a RIGHT to walk around with no pants, I DESERVE to have no pants"; it's shameful. But we don't see this in the moment it happens because anger reduces the clarity of our perception. Breathing meditation also helps (anxiety and anger tend to go together).
In one sutta, the Buddha says that the solution when anger arises is to also recognize, "What more can I expect?" (Everything arises because of cause & effect, anything which happens is either my own kamma, or the kamma of another -- so long as I am within Samsara, how can I not expect to suffer?)
The best things in life aren't things.