We often hear that libertarians advocate the gold standard. This is certainly true, but it is important to understand why and what the true position is for a radical free market advocate.
As a libertarian and a follower of Austrian free market economics, I am in favor of a completely free market in money and banking. Would we be better off under a government run gold standard? Probably yes. Would we be even better off if the government didn't involve itself in money at all? Yes.
For someone who holds radical free market beliefs, then the maximum role, if any, that the government should play in the money business is to protect people from force and fraud. Anything beyond this and the government will use this power for evil purposes.
The reason that you will hear so many libertarians advocate a gold standard is because gold would most likely be the money of choice in a free market. Gold and silver have been used as money for thousands of years. Paper money is a recent thing in a long history of money.
Gold was chosen by the market to serve as money because of its properties. It has a high value (this is why bricks or iron are not used as money). It is divisible without ruining the value (this is why diamonds aren't used as money). It is durable. It has longevity (this is why milk is not used as money). For these and other reasons, gold (and to a lesser extent silver) have great qualities to be used as money.
The most important quality of gold and silver to distinguish them from paper currencies is that they cannot be created on a computer or on a printing press. The government can simply create fiat money out of thin air. To obtain gold and silver, it usually involves intense labor and the supply tends to be very limited. So while you can have inflation of gold or silver (an increase in the supply), it is not controlled by politicians.
So as libertarians, we really shouldn't advocate a gold standard as it might imply that we think the government should manage it. For a truly free market, it is the marketplace that should decide on what will be used as money. Most likely, I would bet my fiat money that the market would choose gold again.