Chinese bronze coin from the Han Dynasty
Money is basically an agreement between people. It is an agreement that this much of something (usually some kind of metal gold, silver, or bronze) will be worth this much bread, and this much cheese, and this many slaves. People also used paper as money, or cocoa beans, or cowrie shells. Anything small, not too heavy, and fairly rare will work.
Coins with guarantees were invented around 650 BC. This kind of coin is marked with a promise by somebody (often a government) that this coin is worth what it says it is worth. So you don't have to weigh each coin before you accept it (if you trust that government). The first coins of this kind were from Lydia, in West Asia. They were used to pay mercenary soldiers. But many people preferred to keep on using mainly credit for trading instead.
A Lydian gold coin
Greek coin from Corinth
When governments began to require people to pay their taxes in money, gradually metal coins became common all over Europe, Asia, and Africa ( except for central Africa and South Africa). In South America, the Aztec empire collected taxes in cocoa beans, in the same way, starting about 1400 AD.
The governments that minted these coins figured out that if they didn't have enough money, they could mix the gold with more silver to make it go further, or mix the silver with more bronze. That way they could make more coins with the same amount of metal, and have more money to pay their soldiers with. The Romans did this in the 200s AD.
Roman silver coins from the 200s AD
But of course people soon figured out that these coins weren't really worth what the government said they were worth, and then they didn't want to take those coins in stores. Or they demanded more coins, so it would be the same amount of gold or silver as before.
To find out more about money, check out these books from Amazon.com or from your library:
Eyewitness: Money, by Joe Cribb (2000). Not the best in the series, but still a good introduction to exchange systems for kids.
The History of Money: From Sandstone to Cyberspace, by Jack Weatherford (1998). Great on what money is, and how it has changed over time - some conclusions are controversial.