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A Roman denarius, a standardized silver coin.
It was the discovery of the touchstone that paved the way for metal-based commodity money and coinage. Any soft metal can be tested for purity on a touchstone, allowing one to quickly calculate the total content of a particular metal in a lump. Gold is a soft metal, which is also hard to come by, dense, and storable. For these reasons gold as a money spread very quickly from Asia Minor where it first gained wide use, to the entire world.
Using such a system still required several steps and some math. The touchstone allowed you to estimate the amount of gold in an alloy, which was then multiplied by the weight to find the amount of gold alone in a lump.
To make this process easier, the concept of standard coinage was introduced. Coins were pre-weighed and pre-alloyed, so as long as you were aware of the origin of the coin, no use of the touchstone was required. Coins were typically minted by governments in a carefully protected process, and then stamped with an emblem that guaranteed the weight and value of the metal. It was however extremely common for governments to assert that the value of such money lay in its emblem and to subsequently debase the currency by lowering the content of valuable metal.
Although gold and silver were commonly used to mint coins, other metals could be used. Ancient Sparta minted coins from iron to discourage its citizens from engaging in foreign trade. In the early seventeenth century Sweden lacked more precious metal and so produced "plate money," which were large slabs of copper approximately 50cm or more in length and width, appropriately stamped with indications of their value.
Metal based coins had the advantage of carrying their value within the coins themselves — they induced on the other hand manipulations: the clipping of coins in attempts to get and recycle the precious metal. The bigger problem was the simple co-existence of gold, silver and copper coins in Europe's nations. English and Spanish traders valued gold coins at a higher rate of silver coins than their neighbours would do, with the effect that the English gold-based guinea coin began to rise against the English silver based crown in the 1670s and 1680s and with the consequence that silver was ultimately pulled out of England for dubious amounts of gold coming into the country at a rate no othe European nation would share. The effect was worsened with Asian traders not sharing the European appreciation of gold altogether — gold left Asia and silver left Europe in quanties European observers like Isaac Newton, Master of the Royal Mint observed with uneasiness.
Stability came into the system with national Banks guaranteeing to change money into gold at a promised rate, it did, however, not come easily. The Bank of England risked a national financial catastrophe in the 1730s when customers demanded their money to be changed into gold in a moment of crisis. Eventually London's merchants saved the bank and the nation with financial guarantees.
See also: Roman currency, coinage metal, for conversions of the European coins before the introduction of paper money: The Marteau Early 18th-Century Currency Converter.
An example of representative money, this 1896 note could be exchanged for five US Dollars worth of silver.
The system of commodity money in many instances evolved into a system of representative money. In this system, the material that constitutes the money itself had very little intrinsic value, but none the less such money achieves significant market value through being scarce as an artefact.
Paper currency and non-precious coinage was backed by a government or bank's promise to redeem it for a given weight of precious metal, such as silver. This is the origin of the term "British Pound" for instance; it was a unit of money backed by a Tower pound of sterling silver - hence the currency Pound Sterling.
For much of the nineteenth and twentieth centuries, many currencies were based on representative money through the use of the gold standard.
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