If you talk about singular good as in your title the answer is demand and supply. However, from body of your question it looks like you are interested in knowing how the aggregate prices are determined.
Aggregate price level is determined on money market. It depends on supply and demand for money and it is given by:
$$\frac{M}{P} = L(Y,i) \implies P = \frac{M}{L(Y,i)}$$
$M$ is the money supply, $P$ price level and $L$ demand for money that depends positively on real output/income/aggregate spending (they are all the same thing from macro perspective) $Y$ and negatively with interest rates.
My guess is currency is actually like a “gold standard” but distributed - there is no rule that a unit equates to one substance - it is simply permitted for the value of commodities to organically arise given however much people are willing to exchange them for.
No. Under gold standard the value of commodities can also organically arise.
The difference is that with gold standard a paper money is on fixed exchange with gold. So in essence paper money just serves as token for gold and in essence gold is used as money to purchase goods and services.
However, economically there is no reason why money should be made out of precious metals. Indeed in the past civilizations used stones or shells as a money as well. Ultimately the role of money in economy is to serve as a 1) medium of exchange, 2) unit of account 3) store of value.
In essence anything can be used for 1 and 2, you could use even paper clips or bags of dirt from your garden. The issue is with 3, advantage of a gold was that generally speaking it use to be good store of value. However, even paper currency can serve as a good store of value as long as value of a currency (which can be think of as $1/P$) is kept stable by appropriate macro policy (via $M$ and $i$ controlled by central bank - mostly the $i$ nowadays). Hence wasting industrially useful commodity such gold makes no sense nowadays. Pieces of paper with dead presidents or even bits can do the same job that gold used to and this does not tie up commodity with important industrial uses in monetary system.
But then, how do you decide how much of a currency a society should have?
That depends on what society wants price level $P$ to be.
And why do the values of currency somehow act erratic, such as with inflation?
Because if you look at the equation:
$$ P = \frac{M}{L(Y,i)}$$
you see that $P$ (remember value of the currency can be thought of as $1/P$) depends on money supply and money demand which depends on real output and interest rates. Real output changes as economy goes through business cycle and sometimes can change suddenly (e.g. the sudden big drop during Covid 19 crisis).
Money supply and interest rate are ultimately controlled by central bank, but this control is imperfect. It's not like central bank can just type $M$ and $i$ into computer. Usually central bank will set interest rate on its reserves and when they set it low private banks lend more and when they lend more they also draw more on CB reserves and all this increases amount of $M$ in the economy. It is not easy to predict exactly by how much decrease in interest rate expands money supply and vice versa. Central banks can also increase $M$ directly by buying assets with new reserves but that happens less often.
Next, the parameters of the economy can change. For example, money demand (assuming its linear) could be given by $L= \alpha Y - \beta i$ and the parameters alpha and beta can change over time.
Finally, the equation above is an equation you would find in a bachelor level textbook. Things are more complicated in real life. If you would look into graduate level versions you would see that what matters is not just what actual real output, money supply or interest are but also what the expected real output, money supply or interest is. When people's expectations change then even if no real change occurred price level in economy can change still.
And, are there any good examples of a smaller group of people inventing a micro-currency between each other?
If by micro-currency you mean currency used by just small group of people, there are examples of prisoners in WWII POW camps developing currencies based on alcohol, chocolate or cigarettes' as money (see Burdett et al 2001).
