The worth of the coins was based on the weight and material(s) of the coin. Currency was not standard throughout the City-states, but currency from Aigina, Kyzikos, and Athens could be used most everywhere. This is comparable to our society where most places accept credit cards, and most international exchange is done in American Dollars, Euros, or Japanese Yen.
Most money was made of silver, but coins of small denominations for use locally could be made out of copper. The coins were beautifully crafted, but not carved by hand. The Greeks employed molds, which they either poured or pressed molten metal into. Americans also employ presses with molten metal to produce money in mints. We also have many different types of coins, where purity, type and weight of the metal determines the coin's denomination. Unlike the Greeks, however, we also use paper money, and our government issues only one system of money for use throughout the country, and most vendors don't accept money from different countries, unless you happen to be close to the border.
Banking / Trade:
Many different types of coins led to the first system of banks and money-exchange. Like our society, people paid property taxes, and got loans. Loaned money earned interest. In Athens, the interest rate for loans was about 12 percent, which is comparable to our own.
What the Greeks could not produce or grow they traded for. Market places could be found in every city, with domestic as well as foreign items for sale. Unless you had money, though, you only had what you made or grew, and little else. Like the American society, the rich controlled much of the economy, and the poor just had to live with the results.