Politics

Politics is the branch of philosophy that defines the principles of a proper social system. Objectivism holds that its subject matter is one question — when may force be used among men — and that its answer is a single principle: force may be used only in retaliation, and only against those who start it.

“The source of the government's authority is "the consent of the governed." This means that the government is not the ruler, but the servant or agent of the citizens; it means that the government as such has no rights except the rights delegated to it by the citizens for a specific purpose.”
~ Ayn Rand, "The Nature of Government", The Virtue of Selfishness

Politics is derived, not primary

Objectivism treats political conclusions as consequences of the ethics, which is itself a consequence of the metaphysics and epistemology. Arguing politics without that base is what Rand called dealing in floating abstractions: "freedom" and "rights" become slogans that each side defines to suit itself.

The derivation is short:

Man's means of survival is reason, and reason is exercised by choice. Nobody can think for another person and nobody can be made to think.
Physical force is the one thing that can stop this. A man with a gun to his head can be made to act, but he cannot be made to judge; force does not defeat a mind, it suspends it. This is why the initiation of force is the fundamental political evil rather than one wrong among many.
What a man needs from other men, therefore, is the absence of force — freedom of action within his own sphere.
The principles defining that sphere are rights. They are moral principles applied to a social context, not grants from a state or a majority.

Everything else in politics follows: which functions belong to a government, what a constitution is for, why capitalism is the only social system consistent with the ethics.

Rights

A right is a sanction to freedom of action, not a claim on goods or on other people's effort. The right to life is the right to the actions a life requires; the rights to liberty, property and the pursuit of happiness are its applications. The right to property is the right to the results of one's actions, without which the others are declarations of intent.

The only obligation a man's rights impose on anyone else is abstention: leave him alone. A supposed right that requires someone else's labour is not a right, because it cannot be held by everyone at once. See Rights.

Rights are inalienable in the sense that they can be violated but not annulled. A man under a dictatorship still has them; the dictatorship is in the wrong.

The individual and the group

There is no collective consciousness. Groups think only in the sense that the individuals composing them do, and every advance in human knowledge was made by a particular mind. A group therefore has no rights beyond those of its members, and can acquire no authority its members do not have. If one man may not seize another's property, ten million may not either, and calling the result "the public good" changes nothing except who is being sacrificed. See Individualism and Collectivism.

The proper social system

Laissez-faire capitalism is the system that follows: all property privately owned, the state separated from economics on the same grounds that it is separated from religion, and the government restricted to the police, the courts and the armed forces. Its defence in Objectivism is moral before it is economic — that it is the only system that treats men as ends in themselves — and Rand argued that its practical success is a consequence of that, not an accident.

Common misunderstandings

That Objectivism is a form of anarchism. It is not. Competing agencies with the power to use force are not a free market but a civil war in slow motion; the argument for government is precisely that retaliatory force must be placed under objective law. See Anarchism and Government.
That it is the same as libertarianism. Rand's objection was not to the political conclusions but to advancing them without a philosophical base, which she held leaves them defenceless. See Libertarianism.
That "freedom" means democracy. Unlimited majority rule is a way of deciding who wields power, not a limit on what power may do. A vote does not create a right to violate one. See Democracy and Elections.
That rejecting the initiation of force means pacifism. Retaliatory force is not merely permitted but required of a government; the distinction is between starting force and answering it.
That fraud is a separate case. Fraud is treated as an indirect use of force: obtaining a value by misrepresentation is taking it without the owner's actual consent.

Discussion

References

Rand, Ayn. "Man's Rights" and "The Nature of Government", The Virtue of Selfishness.
Rand, Ayn. "What Is Capitalism?", Capitalism: The Unknown Ideal. New American Library, 1966.
Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapter 10.