Ne he didn't. Nixon did. Pick up a damn book.
Not exactly. It's more complex than that. Nixon dealt the final blow, but getting us off the gold standard absolutely started with FDR.
A little history:
In the mid-1800s, most countries wanted to standardize transactions in the booming world trade market. They adopted the gold standard, which guaranteed that any amount of paper money could be redeemed by the government for its value in gold.
In 1861, U.S. Treasury Secretary Salmon Chase printed the first U.S. paper currency. The Gold Standard Act was passed in 1900. At this time, the value of all American currency was to be based on actual gold.
In 1933, FDR disallowed the redemption of dollars for gold. This was the first major blow to the gold standard. After all, if paper money is to be based on a gold standard, that means nothing if one could no longer redeem dollars for gold.
In 1934, the Gold Reserve Act prohibited private ownership of gold. It allowed the government to pay its debts in dollars, not gold. FDR was authorized to devalue the gold dollar by 40%. He increased the price of gold, which had been $20 per ounce for 100 years, to $35 per ounce. The government's gold reserves increased in valued from $4billion to $7.3. This effectively devalued the dollar by 60%.
It is not unreasonable to say that FDR was the first to take us off the gold standard, because that is effectively, if not formally, exactly what he did.
Then, in 1946, the Bretton Woods System was enacted. Under this agreement, central banks had to maintain fixed exchange rates between their currencies and the dollar. They did this by buying their own country's currency in foreign exchange markets if their currency became too low relative to the dollar. If it became too high, they'd print more of their currency and sell it.
The formal end of the gold standard came in 1971. All formal links between major world currencies and actual commodities were broken with this change. On August 15, 1971, he changed the dollar/gold relationship to $38 per ounce. More importantly, the Fed stopped redeeming dollars with gold. The U.S. government repriced gold to $42 per ounce in 1973, and then decoupled the value of the dollar from gold altogether. The price of gold quickly shot up to $120 per ounce in the free market.
That was the final nail in the coffin of sound money.