How Exchange rate is Determined?

There is nothing extravagant to tell you as the rate is determined by market forces just like the price of goods and commodities is fixed. The value of any currency is based on the demand for it. If the people buy more of particular currency, value of that currency increases and vice versa. There are few other factors that play a role in determining the exchange rate when you leave the currency value to the market forces & the list is as follows:
Growth of the Economy
Strength of the Economy including export & import
Public Debt
Interest Rates
Speculation & fear

If all these factors are favorable, people across the world get confident about the stability of a particular country & investment climate, which creates the demand of the currency.