Private Currency

Libertarians and the like will enjoy this notice: there is no law preventing you from producing a private currency. One of your own issue, backed by gold. There's no guarantee that anyone would accept it. (I wouldn't.)
When I buy things, I pay with US Dollars. Either directly by handing over notes, or indirectly via a credit card, which involves a series of bank transfers. These dollars are valuable basically because the US government has a monopoly on their production, and because the government says they are. They are "legal tender," the denomination and payment instrument of debt. That is to say, if I owe someone money, they have to accept the notes as payment or the debt is void. If they demand I pay in gold bars, I can take it to court and tell them "Well, I tried to pay with these dollars, he didn't want them" and then they would rule that I don't owe money after all.
Libertarians dislike the idea of legal tender, as they want to neuter the government to the point of which it could not enforce such a decree. They perceive only things backed by metal or some other such tangible good, to be of value.
So logistically, to have your own currency, you'd need a printing press, intricate designs, some sort of anti-counterfeiting system so that it's difficult for other people to copy your notes, and a stash of gold so that people can redeem your notes at their request. They should not be confused with US Dollars, and for safety's sake, should be of a very different design and size.
As a precedent for this, Scottish-printed notes in the UK are not legal tender in Scotland. In spite of this, a number of shops will accept them anyway, as if it were a check written out to them.
In the past, currency issuing was generally done by banks, who made them as a symbolic representation of a deposit, and then people exchanged them to save themselves the trouble of retrieving the deposit to hand over to the shopkeeper, who probably planned to spend it on something else anyway. The note was lighter and more portable than the original deposit, and easier to handle commerce in. Governments got into the act later.
Now as for accepting, I think it would go over about as well as a foreign-issued currency. In theory I could pay for my groceries in British pounds, or Mexican pesos, or Chinese renminbi, but in practice the store's probably going to demand US dollars, because it can use those right away.