Bitcoins are not backed by another currency or commodity. Bitcoins' value solely derives from their scarcity and utility. As their value doesn't derive from backing, the exchange rate is discovered by the market for example through trade on Bitcoin exchanges. Also see: Where do bitcoins come from and what gives them their value?
Fiat currencies such as the US Dollar, Euro, or Renminbi are not backed by commodities either: They are backed by the power of the state distributing them as well as their citizens faith in the currency. The Gold Standard was discontinued in 1931, the succeeding Bretton Woods system that fixed exchange rates of different currencies and their gold price was abolished in 1971.