If the exchange rate of the national currency is depreciating, what actions must the nation's Central Bank take in the foreign exchange market (if any) to restore parity?  

Actions taken by Central Banks to restore currency value

1. Sell foreign exchange assets, purchase own currency
2. Raise interest rates (attract hot money flows
3. Reduce inflation (make exports more competitive
4. Supply-side policies to increase long-term competitiveness

Step-by-step explanation

Sell foreign exchange assets, purchase own currency: This strategy involves a country selling foreign assists like the treasury bonds and treasury bills to the foreign countries to reduce the value of foreign country currency while increasing that of home country. For example China has over 1.4 Trillion US government bonds, if say Chinas currency reduces in value they would sell back the bonds to the US government which would depreciation in the dollar and in turn would increase the value of Chinese Yuan. Thus countries uses this strategy to gain value on the decreased currency value.

Raise interest rates: The central banks raises interests rates, higher interest rates would attract some hot money flows. Hot money flows occur when banks and financial institutions move money to other countries to take advantage of a better rate of return on saving. Given interest rates are close to zero in the US, higher interest rates in developing countries give a significant incentive to move money and savings there. The central bank of a country can move more money into other better performing foreign countries economy like the United States so as to gain a lot of incentive which in turn improves the value of the currency as the money kept multiplies significantly.

Reduce inflation: To increase the value of a decreased currency, the government through its central bank will reduce inflation so that the country's good become more attractive and demand will rise.. Lower inflation tends to increase the value of the currency in the long term. Inflation on the other hand is reduced by the central implementing the fiscal and monetary policies. 

Supply-side policies to increase long-term competitiveness: To increase exchange rate, countries will need a combination of low inflation, productivity growth, economic and political stability. Thus to increase the value of the currency in the long-term, the government through its Central Bank will need to try supply-side policies to increase competitiveness and cut costs of production, for example, privatization and cutting regulations may help the export industry become more competitive in the long-term. Higher exports means more foreign exchange thus high values of currency.