I want to take a stab at this question, even though so many answers have already been supplied. This is different, and adds something unique, I think:
Under what circumstances does God act on His anger, you ask?
Every time He feels it.
The Bible teaches that you should never sit on your anger and do nothing about it; nor does it imply that when God gets mad He just sits there and stews and stews until either you straighten up or He boils over, whichever comes first, but nothing but either of those two.
Rather, it always advises full attention and prompt action at the onset, along the lines of "do nothing until you've resolved it," "resolve it quickly and ahead of anything else," "consider what you'll lose if you don't," and "consider what you'll gain if you do." You'll note that the things you can lose and the lay which you can gain are not small things, ranging from death to life and all in between.
God does with His anger what He does with it; but, here's a few of His insights and recommendations on it for us (extrapolate freely; God practices what He preaches):
On the consequences of anger:
For man’s anger does not promote the righteousness God [wishes and requires]. [James 1:20]
Cease from anger and forsake wrath; fret not yourself—it tends only to evildoing. [Psalm 37:8]
A man of wrath stirs up strife, and a man given to anger commits and causes much transgression. [Proverbs 29:22]
Do not be quick in spirit to be angry or vexed, for anger and vexation lodge in the bosom of fools. [Ecclesiastes 7:9]
He who is slow to anger has great understanding, but he who is hasty of spirit exposes and exalts his folly. [Proverbs 14:29]
On the benefits of subduing anger:
He who is slow to anger is better than the mighty, he who rules his [own] spirit than he who takes a city. [Proverbs 16:32]
Good sense makes a man restrain his anger, and it is his glory to overlook a transgression or an offense. [Proverbs 19:11]
On avoiding anger:
Make no friendships with a man given to anger, and with a wrathful man do not associate. [Proverbs 22:24]
A soft answer turns away wrath, but grievous words stir up anger. [Proverbs 15:1]
Fathers, do not irritate and provoke your children to anger [do not exasperate them to resentment], but rear them [tenderly] in the training and discipline and the counsel and admonition of the Lord. [Ephesians 6:4]
Be angry, and do not sin: do not let the sun go down on your wrath. [Ephesians 4:26]
On the characteristics of a true child of God, as they relate to anger management:
I desire therefore that in every place men should pray, without anger or quarreling or resentment or doubt [in their minds], lifting up holy hands. [1 Timothy 2:8]
A [self-confident] fool utters all his anger, but a wise man holds it back and stills it. [Proverbs 29:11]
But now put away and rid yourselves [completely] of all these things: anger, rage, bad feeling toward others, curses and slander, and foulmouthed abuse and shameful utterances from your lips! [Colossians 3:8]
Let all bitterness and indignation and wrath (passion, rage, bad temper) and resentment (anger, animosity) and quarreling (brawling, clamor, contention) and slander (evil-speaking, abusive or blasphemous language) be banished from you, with all malice (spite, ill will, or baseness of any kind). [Ephesians 4:31]
On the characteristics of a child of Belial, with respect to lack of self-control and anger:
Idolatry, sorcery, enmity, strife, jealousy, anger (ill temper), selfishness, divisions (dissensions), party spirit (factions, sects with peculiar opinions, heresies). [Galatians 5:20]
On characteristics of God’s anger, which one should mimic in all respects:
For His anger is but for a moment, but His favor is for a lifetime or in His favor is life. Weeping may endure for a night, but joy comes in the morning. [Psalm 30:5]
But He, full of [merciful] compassion, forgave their iniquity and destroyed them not; yes, many a time He turned His anger away and did not stir up all His wrath and indignation. [Psalm 78:38]
The Lord is long-suffering and slow to anger, and abundant in mercy and loving-kindness, forgiving iniquity and transgression; but He will by no means clear the guilty, visiting the iniquity of the fathers upon the children, upon the third and fourth generation. [Numbers 14:18]
On your right to be angry:
What right can a sinner have to yield to impatience or anger, when mercifully corrected for his sins? [Psalm 38:12-22]