Happiness

Happiness is the state of consciousness that proceeds from the achievement of one's values. In Objectivism it is the moral purpose of a person's life — not the standard by which values are chosen, which is life itself, but the result of choosing and achieving them correctly.

“Happiness is that state of consciousness which proceeds from the achievement of one's values.”
~ Ayn Rand, Atlas Shrugged

Purpose and standard are not the same thing

The distinction is the one most often collapsed, and the whole position depends on it.

The standard of value is man's life: the measure against which a thing is judged good or bad. It answers "by what criterion?"
The moral purpose is one's own happiness: the reason a person acts at all. It answers "for whose sake?"

Reversing them produces hedonism, which takes the feeling as the criterion and so has nothing to say about which desires are worth acting on. Objectivism's position is that happiness is an effect with a cause, and the cause is the achievement of values that a person's life actually requires. Feeling good is not evidence that a value has been achieved; it is what achieving one feels like. See Emotions.

Emotions follow from what one values

Emotions are automatic responses to a person's own value-judgments — an estimate, made instantly, of whether something confronting him furthers or threatens what he has accepted as good. They are not tools of cognition; see Reason-Emotion Dichotomy.

Two consequences bear on happiness directly:

One's emotional capacity is set by one's values. A person who has adopted values that cannot be achieved, or that conflict with each other, has built a mechanism that will generate frustration no matter how hard he works. This is why Objectivism treats the choice of values as a practical question rather than a matter of taste.
Happiness cannot be pursued directly. It is not itself a value one can act to gain; it is the accompaniment of acting to gain other things. Attempting to produce the state without the achievement is what drugs, evasion and manufactured distraction attempt.

Rand's term for the achieved condition was "non-contradictory joy": a happiness that does not require avoiding any part of one's own knowledge, and that costs nothing to anyone else.

Common misunderstandings

That Objectivism is hedonism. Hedonism makes pleasure the standard. Objectivism makes life the standard, and holds that whim-directed pleasure-seeking generally destroys the conditions of happiness. See Subjectivism.
That "do what makes you happy" is the ethics in short form. It is not, because it says nothing about which things will. The work is in identifying the values, which is what the virtues are for.
That happiness means the absence of pain. Suffering is possible in any life, and Objectivism does not treat it as a moral failure. What it denies is that suffering is the normal or proper state of man.
That it is a duty to be happy. Objectivism rejects unchosen duties. The claim is conditional: if a person chooses to live, happiness is what a life lived successfully produces.

Discussion

References

Rand, Ayn. "The Objectivist Ethics", The Virtue of Selfishness. New American Library, 1964.
Branden, Nathaniel. "The Psychology of Pleasure", The Virtue of Selfishness.
Rand, Ayn. Atlas Shrugged — Galt's speech, on happiness as the purpose of a life.
Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapter 9.

External links

Happiness at the Ayn Rand Lexicon