Libertarian is also known as Classical Liberalism, Randian/Randianism (after Ayn Rand), but is just the belief that liberty should be the core principle of their philosophy, seeking to maximize political freedom and autonomy, emphasizing freedom of choice, voluntary association and individual judgment (and responsibility/accountability). In Europe, this would be left wing, in the U.S. it is right wing. (Technically, Libertarian can mean the party, or a form of Classical Liberalism).
The basics are Thomas Jefferson was a libertarian, as were most of the founding fathers. Which means most libertarians are conservatives, in that they want to go back to when the U.S. had more individual liberties, smaller federal government (more state governmental control), lower taxes, more opportunities, and less regulations. There's a huge spectrum of how far back, and in what areas first. And it's important to remember that this is opposed to most European conservatives: where when they want to go back, it's often back to more imperial or monarchistic autocracy or centralized control (our histories are different, so back means different things).
Libertarians are "classical liberals". Basically, what liberal (where libertarian came from) originally meant is, "Liberty": maximizing autonomy, freedom of choice, and the primacy of individual judgment. Around the turn of the 19th century, American progressive socialists started to usurp the name liberal, and re-invent it as meaning themselves (heavy state control and what federalism used to mean): even-though everything the left stood for was the opposite of classical liberalism. Since this didn't take root in Europe, "liberal" means opposite things in the U.S. and Europe (generally American libertarian is what Europe means with liberal -- though Americas misuse of the term has muddied the waters as Europeans have started using it wrong as well).
Here's a list of things that are, or are not, Libertarian -- and what the term or philosophy means. Libertarian : 8 items