The Chinese government sets it for the renminbi and there are at least a dozen other governments that set the exchange rates for their own currencies:
http://en.wikipedia.org/wiki/Fixed_exchange_rate

Most countries allow their currency's exchange rate to float, but occasionally intervene:
http://en.wikipedia.org/wiki/Floating_currency

Krugman argues that it is really the currency speculators who set the exchange rates for those that float:
http://www.econlib.org/library/Enc/ExchangeRates.html

For a description of the foreign exchange markets, you can look at:
http://en.wikipedia.org/wiki/Foreign_exchange_market

For "nitty gritty details" you'll have to do some work and take some time - perhaps work for one of the major international banks or international exchanges for a while?