What Do We Mean By Justice?" "Wealthy GOP (Libertarian) Donors Backing Same-Sex Marriage" "The Curious Popularity of Ayn Rand"). As I've noted in those posts, libertarians believe in limited government. They favor free markets and oppose most government regulation. They contend that each of us has a fundamental right to do whatever we want with the things we own as long as we respect the rights of others to do exactly the same thing. Thus, they tend to oppose (a) laws that protect people from themselves (e.g., seatbelt laws), (b) laws that promote virtue or express the moral convictions of the majority (e.g., pro-life anti-gay rights legislation), and (c) and laws that redistribute income and/or wealth (e.g., income taxes used to help the poor in some respect).
Although most libertarians favor limited government, they still think government is important and has a role (e.g., in protecting property rights). However, there are a handful who take individual freedom to the nth degree, and these folks can be found at the Porcupine Freedom Festival (aka, the PorcFest) where people try to live without government interference, where you can use slivers of silver to buy uninspected bacon, where 9-year-olds can sell you alcohol, and where you can chat with people who think we should return to the gold standard and abolish the IRS (not to mention the Federal Reserve).
If you are like most folks and don't want spend a week at the festival, you can learn about it from a recent NPR Planet Money podcast ("Libertarian Summer Camp"). You can either listen to the podcast at the Planet Money website or download it from iTunes.