Anger in Buddhism is defined here as "being unable to bear the object, or the intention to cause harm to the object." Anger is a stronger exaggeration of aversion (dosa) and in meditation is considered one of the Five Hindrances.
Buddhist monastics are full time practitioners of the Dharma who also sometimes get angry. However, the difference is that a spiritual person is aware of the arising emotion, the danger in, and the escape from this and other unchecked hindrances.
How can it be handled? In response to the question, "Is any anger acceptable in Buddhism?' the Dalai Lama answered:
Buddhist scholar and author Geshe Kelsang Gyatso has also explained the Buddha's teaching on the spiritual imperative of identifying anger and overcoming it by transforming difficulties:
When things go wrong in our lives and we encounter difficult situations, we tend to regard the situation itself as our problem. But in reality whatever problems we experience come from the side of the mind. If we responded to difficult situations with a positive mind they would not be problems for us. Eventually, we might even regard them as challenges or opportunities for growth and development. Problems arise only if we respond to difficulties with a negative state of mind. Therefore, if we want to be free from problems, we must transform our mind (How to Solve our Human Problems).
The Buddha pointed out some of the immediate harm that comes from anger, as opposed to the benefits of cultivating loving-kindness:
An angry person becomes ugly and sleeps poorly. Gaining a profit, one turns it into a loss, doing damage in word and deed. A person overwhelmed by anger destroys a store of wealth. Maddened by anger, one destroys one's status. Relatives, friends, and colleagues avoid the angry person. Anger brings on loss. Anger inflames the mind. One does not realize that danger is born from within. An angry person does not know that benefit is born there, too. An angry person does not see the Dharma. A person conquered by anger is in a mass of darkness. One takes pleasure in bad deeds as if they were good. But later when anger subsides, one suffers as if burned. One is spoiled, blotted out, like fire enveloped in smoke. When anger spreads, when a person becomes angry, one has no shame, no fear of wrongdoing, is not respectful in speech. For a person overcome by anger, nothing gives light ("Seven Things that Befall an Angry Person," Kodhana Sutra, AN 7.60).
So how does one easily manage anger? The first thing is to recognize it as a problem. So long as we think it's a benefit -- anger strengthens me, it keeps me alive, it motivates me to take action, and so on -- we will not seek to overcome it. However, when we recognize that in addition to any benefits, there are grave dangers in all anger, we can begin to eagerly take the steps: