A good book covering the subject is The History of Money (Jack Weatherford). Money was has had a tradition of being valuable in its own right (gold and silver coin), and eventually banks created paper money that represented an amount of gold held in reserve.

The Bank of England, was at first a private entity (established in 1688) and was only nationalized in 1946[1]. The notes they issued were backed by deposits of coin, gold, or silver. They broke with the gold standard in 1931, and it's then we see money tied not to a specific asset, but rather as a debt instrument; it's valuable only because someone promises to pay you back.

When the debtor is a nation-state, we have fiat money, and the money is backed only by the faith and credit of the nation who issues it.

As Weatherford's book points out, fiat currency was not invented by the British, as the Chinese were using a similar system in the 1st or 2nd century, and continued to use a paper money system until 1399. Abuses destroyed the value of the paper currency, and it did not reappear in China until the 20th century.

[1] http://en.wikipedia.org/wiki/Bank_of_England

In the US, during the early 19th century, state-chartered banks (and other countries, such as insurance companies and railroads) would issue their own notes. These were not, technically speaking, money, but they were used as such, because there just wasn’t enough gold and silver coin circulating in the country to be practical for commerce.

Cf. the book A Nation of Counterfeiters.

As with many things in history, I don't think there is a single year that we can point to as the turning point, since it's a somewhat gradual shift.

Think about it this way - a few hundred years ago, it was commonplace to pay dues to the government using precious metals (like gold). In some parts of the world, this is still the case, but in the majority of the developed world, public and private debts are paid with money that gets its value by fiat.

This change can't happen overnight, even if you force it to; if people continue to accept gold (for example) has having liquid value, then it will continue to be used as a currency.

I wouldn't even use the beginning or end of Bretton Woods as the turning point (though it was certainly a turning point), because the point is less whether people can convert currency to gold than it is a question of whether they do.