There are two ways of backing currency with gold. One is to increase the price of gold so that it "covers" all the money in the world. The other is to set the price of gold and adjust the money supply to fit the stockpile of gold.
A short post can't get into all the ramifications, but we can get an idea of the magnitude of the changes required.
The first challenge is finding out how much gold there is in the world. Because of mining and usage, this number is always changing. The number I'm using comes from Wikipedia showing 174,100 metric tons. This translates into about 5.6 billion troy ounces.
Not all that gold is available for use as money. I get varying answers from half to two-thirds being available. This give a range of 2.8 to 3.7 billion troy ounces available to use as money.
The most recent number for all the money in the world is a 2012 estimate from the CIA World Factbook, expressed in US Dollars, totaling $81.7 trillion.
Taking the $81.7 trillion and dividing by 3.7 and 2.8 billion troy ounces gives us a range from $22,081 to $29,179 per ounce.
Gold is currently about $1,200 per ounce, so these prices are about 18-24 times current pricing.
The other way of returning to gold backed currency is to set a fixed price per ounce. Before FDR confiscated gold from Americans, the price was set at $20.67 per ounce.
If we take our 2.8 to 3.7 billion ounce supply and multiply by $20.67 per ounce, we get a money supply ranging from $57.9 to $76.5 billion dollars. We then divide by the current money supply of $81.7 trillion to get our exchange rate.
Taking a $100 Federal Reserve Note from today and "exchanging" it for the gold backed dollar of 1933 will net you between 7 and 9 cents.
No matter which method you choose, adjusting prices to match would result in a severe shock to the economy.
Wasn't it fun pretending we were rich by creating money out of thin air?