Money in the sense of exchanging one thing for another has probably been around for as long as humans have lived in organised groups. Very early societies would use a commodity, for example cattle, as a form of currency (ie you might use a fixed number of cattle as a unit of exchange, rather than simply swapping a cow for something else).
The earliest money probably developed as a unit of weight. The shekel, for example, goes back to about 3000 BC and was originally a means of determining the value of a quantity of wheat etc (the British pound originated in the same way and so did some other currencies).
Other societies, for example in very early Chinese culture, used shells and similar objects as units of exchange, and this practice spread to parts of India and elsewhere. This happened from around 2500 BC.
The use of coins and metal money goes back to about 1000 BC and again the earliest examples can be found in China.