How can a government manipulate floating exchange rate?

A government can manipulate floating rate by controlling the interest rate. To increase the exchange rate, ie the value of the currency, the government can increase its interest rate, which attracts foreign investors to save money in the country. To do so, the investors have to buy the country's currency, which increases the demand for the currency. As the demand curve of the currency shifts outwards, the price (the exchange rate) of the currency increases, hence a higher exchange rate. Vice versa for a lower exchange rate.