Because we live in a world of fiat money, it is hard to imagine a society that functions with free money and free markets. Many people, libertarians included, forget that so much of what we are accustomed to only takes place because of fiat money.
Let's imagine a society with a truly free market. If this society had any government, the only thing the government would do would be to protect people and their property and enforce contracts. This means there would be no or minimal taxes and no or minimal government regulations (the market would have regulations). It also means there would be no legal tender laws and no central bank creating money out of thin air.
Now let's say that the free market in this society chooses to use gold or silver (or perhaps both) as money. People would be free to use whatever they want, but most likely one or two things would win out and become money for society. People would obtain gold or silver so that they could save, invest, and buy other things.
For the sake of discussion, let's say that banks did not participate in fractional reserve banking. I would argue that even in a free banking system, banks would keep close to 100% reserves anyway, but either way, let's say for this discussion that all banks kept 100% reserves. Now, this is not realistic, but for discussion sake, let's also say that the amount of money (gold or silver) does not change. There is no new mining and the money stays within this society.
Now, that is a lot of assumptions, but what would this society look like? Besides the fact that it would flourish, there would be a lot of differences with what we have in current day America. For example, we are accustomed to wages going up (at least before a couple of years ago). This would not really happen any longer as a whole, at least not in nominal terms.
Over time, we usually see stock prices go up. We usually see housing prices go up. We usually see the prices of consumer products go up. But this would all go away. Housing might actually get cheaper over time. While stocks would still go up and down, the overall stock market would not likely go up. This is hard to fathom. So why would anyone buy stocks? Well, any one particular stock can go up, but you could still buy index funds because they would pay dividends (especially with no tax on dividends).
This is really tough for people to grasp. Wages would not go up. You would have the same money supply, so how could they go up? Where would the money come from? But this is all ok.
Many people think that as the number of goods and services in society increases, that the money supply must increase to accommodate this. But it just isn't true. What happens is that your money becomes worth more. With the same amount of gold or silver, you can buy more today than you could yesterday. We would live in a world like the electronics industry. Things would get better and cheaper as time goes on. You wouldn't see a rise in nominal wages, but your standard of living would shoot up as your wages could buy so much more.
This is what actually happened in much of 19th century America. Prices actually fell gradually. But it wasn't some scary deflation. It was an increase in purchasing power due to increased investment, technology, and productivity. This is the way it should be. We should expect more for our dollar tomorrow, but instead we get less. We have been brainwashed by fiat money.