Currency exchange values work in two ways. They can work through trade, using supply and demand to determine currency value, or through the valuation of a fixed currency, determined by the ability of that country to keep its currency value pegged at the desired rate against a second currency.
The private currency exchange market, known as FOREX, uses simple supply and demand for currency valuation by having two separate traders complete an exchange. One trader offers to sell the currency at a chosen price. If another trader accepts the currency at that price, then the value of the currency adjusts accordingly. A fair price for the currency is established through a large number of trades. The value is largely determined by the economic strength of the different currencies as well as the buying power of each currency. Because of differing economic strengths, many trades involve one unit of currency traded for multiple units of a second currency.
Fixed currency value is set by the central bank of the country trying to maintain the fixed rate. With a fixed currency, the value of the currency versus the anchor currency never changes. The central bank keeps the valuation even by buying or selling the second currency to keep enough of the second currency on-hand to meet the set rate. For example, a fixed rate of $2 means that the country must buy enough dollars to offer two for every one of its currency.