What determines the demand for and supply of a currency in the foreign exchange market?

Economic policies stated by central Banks and government agencies, economic reports, conditions and other economic indicators.
So anything done from the Central bank affects the supply.. If the CB increase the money supply then the supply curve will shift to the right and vice versa.

Political conditions within and around the country also affect the currency market. Regional, central and international politics cast a profound effect on the currency market.

The Market Psychology and the perception of the traders and buyers also affect the currency market in various ways.