It’s not much different from how the prices of your mangoes are determined, for example. Whether currency movements or prices of mangoes, the most important factor determining their price is the same – market forces of demand and supply.
If the demand for dollars increases, the value of dollar will appreciate. As the quotation for Rs/$ is a two way quote (that is, the price of one dollar is quoted in terms of how much rupees it takes to buy one dollar), an appreciation in the value of dollar would automatically mean a depreciation in Indian rupee and vice-versa.
During turbulent markets, investors usually prefer to park their money in safe havens such as US treasuries, Swiss franc, gold and so on to avoid losses to their portfolios. This flight to safety would lead to foreign investors redeeming their investments from India. This could increase the demand for dollar vis-à-vis Indian rupees.
There are derivative instruments and over-the-counter currency instruments through which one can speculate/ hedge the underlying currency rates. When speculators sense improvements/ deterioration of the sentiments of the markets, they too want to benefit from such rising/ falling dollar. They then start buying/selling dollar which would further change the demand/ supply of the dollar.
Central Bank (RBI) Intervention:
When there is too much volatility in the rupee-dollar rates, the RBI prevents the rates from going out of control to protect the domestic economy. The RBI does this by buying dollars when rupee appreciates too much and by selling dollars when the rupee depreciates significantly.
Imports and Exports:
There are a lot of schemes and incentives for exporters while importers are burdened with many conditions and taxes. This is to protect our economy from high rupee depreciation. Importing foreign goods requires us to make payment in dollars thus strengthening the dollar’s demand. Exports do the exact reverse. So, buy Indian to strengthen rupee.
Public Debt / Fiscal policy:
Whenever our Government fails to match expenses with equivalent revenue, there is a shortage of funds. To finance this, the Government at times opts to borrow money from institutions such as the World Bank and the IMF. This debt, accrued interests, and the payments made, also lead to currency fluctuations.
The prevailing interest rates on the government bonds attract foreign capital to India. If the rates are high enough to cover the foreign market risk and if the foreign investor is comfortable with the fundamentals or credit ratings, money would start pouring into India and thus provide us with a supply of dollars. The down side of increasing interest rates is inflation.