I found this definition on Wikipedia. It outlines a wide range of thought, often contradictory, about what, exactly a libertarian is, so it's not really a definition--more a discussion. To distinguish "libertarian" from "Libertarian," a Libertarian is anyone who has registered Libertarian with the State, or who has contributed to the Libertarian Party. People who hold at least one belief fundamentally at odds with one or more of the really defining beliefs of a libertarian have run for office as Libertarians. Every political group is forced by state laws to accept lunatics as their nominees for just about any political office.
The base-line defining characteristic of a libertarian is that (s)he believes that it is immoral to initiate force to achieve personal or political goals. A "pure" follower of the philosophy of the Democratic Party thinks it's okay to hire folks to shoot you if you don't give over a bunch of your paycheck to support their charities. A similarly-minded Republican will gladly shoot you and your doctor for "killing babies" or "doing dope."
I found it odd, for example that this appears below: "Libertarian historian George Woodcock defines libertarianism as the philosophy that fundamentally doubts authority and advocates transforming society by reform or revolution." About half of everyone falls through that gravel screen. If he's a "Libertarian historian," he's gotta know there's more to it than that.
This statement probably is the truest of all below: "Libertarian schools of thought differ over the degree to which the state should be reduced." I'll venture that libertarians agree that the pursuit of happiness is more often successful under the least coercive of societies.
In the passage from Wikipedia (there are many hyperlinks below; most words that might need further definition are links, and all the footnote numbers are links):
Libertarianism is generally considered to be the group of political philosophies which emphasize freedom, liberty, and voluntary association. There is no general consensus among scholars on the precise definition. Libertarians generally advocate a society with a government of small scope relative to most present day societies or no government whatsoever.
The Stanford Encyclopedia of Philosophy defines libertarianism as the moral view that agents initially fully own themselves and have certain moral powers to acquire property rights in external things. Libertarian historian George Woodcock defines libertarianism as the philosophy that fundamentally doubts authority and advocates transforming society by reform or revolution. Libertarian philosopher Roderick Long defines libertarianism as "any political position that advocates a radical redistribution of power from the coercive state to voluntary associations of free individuals", whether "voluntary association" takes the form of the free market or of communal co-operatives. According to the U.S. Libertarian Party, libertarianism is the advocacy of a government that is funded voluntarily and limited to protecting individuals from coercion and violence.
Libertarian schools of thought differ over the degree to which the state should be reduced. Anarchistic schools advocate complete elimination of the state. Minarchist schools advocate a state which is limited to protecting its citizens from aggression, theft, breach of contract, and fraud. Some schools accept public assistance for the poor. Additionally, some schools are supportive of private property rights in the ownership of unappropriated land and natural resources while others reject such private ownership and often support common ownership instead. Another distinction can be made among libertarians who support private ownership and those that support common ownership of the means of production; the former generally supporting a capitalist economy, the latter a socialist economic system. Contractarian libertarianism holds that any legitimate authority of government derives not from the consent of the governed, but from contract or mutual agreement, though this can be seen as reducible to consequentialism or deontologism depending on what grounds contracts are justified. Some Libertarian socialists reject deontological and consequential approaches and use historical materialism to justify their political beliefs.
Political scholars such as Noam Chomsky assert that in most countries the terms "libertarian" and "libertarianism" are synonymous with left anarchism. It is only in the United States that the term libertarian is commonly associated with those who have conservative positions on economic issues and liberal positions on social issues, going by the common meanings of "conservative" and "liberal" in the United States.