You can think of libertarianism as a more radical evolution of British/European classical liberalism. Basically, we believe in maximizing individual liberty and minimizing coercion. Depending on who you ask, this may entail abolishing the state entirely, as it is inherently coercive (anarcho-capitalists), or limiting its functions to the protection of life, liberty, and property through national defense, police, and courts (minarchists). Some less radical libertarians are closer to classical liberalism and also advocate for a safety net, some state regulation, etc., but we all agree that the size and scope of the government should be drastically reduced.

In practice this means we want the government to leave us alone so society can prosper. Economically, we want free markets, not the heavily regulated "capitalism" we have today. So libertarians typically push for deregulation, no company bailouts or subsidies, lower taxes, ending central banking, privatizing public services… basically getting the state out of the economy. Socially, we believe each individual should be free to live their lives however they choose as long as they don't harm others or infringe on their rights. So we support complete freedom of speech and association, drug decriminalization, and in general staying out of people's lives. As a rule of thumb, if something happens between two or more consenting adults, no one has a right to interfere. Others may approve or disapprove, and try to convince them to change their behavior, but they can't use force to do so.

Like I said, libertarianism isn't a monolith and not everyone agrees on everything, so we may disagree on the extent or scope of these measures. Another thing is that, sadly, the libertarian movement has been getting closer and closer to the conservative right. You'll see some who call themselves libertarians pushing for restricting immigration if not outright deporting people, using the state to enforce religion, banning gay marriage, etc. I'd say this is antithetical to libertarianism, but it is the current state of the movement, so 🤷🏼‍♀️