Well, it's fairly simple in a way. True libertarianism is based in Natural Rights, which is the basically boils down to the idea that everyone has the right to do whatever they want *as long as* they don't directly harm others, defraud/cheat them, or damage/take their property.
So that means no drug wars, no victimless crimes, no "crimes against the state", no thought crimes. Freedom of speech, private property, privacy, etc. The Constitution is a libertarian document. It defines the role of the state, if there is to be one, as the defense of life and property and little, if anything more. That governments don't have rights, only people have rights and they all have the same rights. They wanted to apply this to slaves, but simply couldn't due to the political climate of the times.
The whole idea is based on rational empathy, which is the natural result of sentience. Because you figure, well, if I want to live, and eat and have freedom, surely other living, sentient beings want the exact same thing, so I should respect their rights as I would have them respect mine.
It also means that people helping people shouldn't be through government, but through individual or voluntary group action. Because stealing from one person to help another isn't ethical or moral. In a way, it loosely follows the teachings of Jesus, to be tolerant, charitable, kind, inviting. In a libertarian world, their might be governments, but there wouldn't be borders. People would be free to live where they wish without having to ask permission from government. You could drink a large soda or smoke a joint. Libertarianism doesn't judge what other people do, as long as they aren't harming anyone. It promotes peaceful trade between countries rather than war. Low, if any, taxes, economic prosperity, and a big, accessible court system to settle disputes. Kinda like Judge Judy on steroids. Go in, pay a small fee, get things settled, move on.
