The core libertarian idea is the Non-Aggression Principle (NAP). It simply means that you have a natural or God-given right to live your life according to your values, without coercion - as long as you do not initiate violence, force or fraud against others. But when someone violates this rule and threatens harm against you or others, you may defend yourself with necessary force and violence. The Non-Aggression Principle is a recipe for how people of difference ideologies can live together in a diverse country like America, and it is a principle that resonates strongly with the philosophy of the U.S. Constitution.
The Constitution restricts government from infringing on our rights. But those rights do not originate in the Constitution. In fact, the 9th Amendment states explicitly that there are rights not mentioned in the Constitution. Our founding fathers understood that human rights ultimately originate from natural philosophy, or from God.
Government by the People
People form governments to protect themselves from violence and abuse. In a democratic system, government derives its authority from the people. For this reason government should not exercise any authority that the people themselves do not have. Protection against violent or malicious criminals comes from the right of self defense. But government should never have the right to take your money and use it for causes you disagree with. For example, if your neighbor is opposed to abortion on principle, you should never make them pay for it via tax dollars. And while you may choose not to smoke marijuana, drink alcohol, or consume sugary beverages in accordance with your own values, these acts should not result in punishment since they do not harm others.
The larger government becomes and the more power it holds, the more it attracts people who want to use that power for their own benefit. From special interest lobbies, to corporate welfare, to a legal system that works to enrich lawyers at the expense of the people at large, We need to shrink the power of government until it fulfills its primary purpose of protecting people from harm.
No one knows what is best for you more than you, and no one knows what is best for your community more than the people who live in it. Good government is as local as possible, so that the people who stand to gain or lose the most are those making the best decisions for themselves and their communities.
Fallible People = Fallible Government
Too often legislators tout their latest cure-all solution to one social problem or another, but when put into practice, their idea falls flat. Top-down one-size-fits-all solutions are rarely the best solutions, or even better than what existed before. Competition among various methods, powered by personal initiative, is the best way to find solutions that work and achieve real progress.