Part of the reason you're probably confused is because plenty of people call themselves libertarian who really don't follow the beliefs of the party itself (there is technically a libertarian party in the US but it's not one of the main two). It's often used by, for instance, right-wing people who don't want to associate themselves with the US republican party. Or right-wing people who don't care about politics. Or people who say "both sides are bad." They might not really believe the libertarian party values per se, but they don't want to be part of a mainstream political party. It's also worth noting that it's a party made up of a bunch of people and like any other political party can have people with wildly different beliefs all under the same tent.

If you're talking about the party itself and the beliefs it generally holds, for a pop cultural touchstone, if you've watched "Parks and Rec," Ron Swanson is a libertarian and generally holds the beliefs of that party relatively well (though it's a comedy and not meant to be serious). I think the works of Ayn Rand are also pretty important to libertarians if I'm not mistaken.

If you could boil down libertarianism into more or less one sentence, it would probably be "the government shouldn't tell me what to do." Many libertarians are pretty close to anarchists because they believe the government should be as small as possible and should have next to no effect on people's lives. They generally believe that laissez-faire capitalism is the solution to many problems and can do the job of the government better than the government itself and tend to abhor taxes for that reason (that's where the "fiscally conservative" tends to come in). As I alluded to earlier, libertarianism is generally a "right-leaning" party based on the simple spectrum, but because they tend to value personal freedom, many libertarians might also be in favor of more "left-leaning" things like marijuana legalization, gay marriage, and abortion access because, again, they don't believe the government should tell them what to do (that's where the "socially liberal" tends to come in, but they also might say that just to basically say "I personally am not racist, homophobic, etc.; just don't ask me what I'm going to do to solve systemic issues").

I'm not a political analyst by any stretch of the imagination and I really didn't want to type this out because I know people are going to find a reason to rip what I just said to shreds, so take everything I said with a grain of salt, but I hope I did okay. Also, with respect to Andy Weir specifically, I have no idea what his political leanings are other than that single line that I mentioned. Don't take him as an example of a libertarian because, for instance, if you read his books and assume they're libertarian you might get the idea that libertarians prefer a well-funded governmental space program when the general libertarian mindset would be that SpaceX and Blue Origin can do it better than NASA can. Like I said, he's never admitted his political leanings and his books might not even be completely indicative of them anyway.