Can someone explain to me exactly how the exchange rate of BTC/USD or BTC/EUR is calculated?
There are people selling bitcoins and people buying bitoins. Sellers want to sell at high prices. Buyers want to buy at low prices. When a seller offer meets a buyer offer, a trade is made. The current price is the price of the last trade.
For example, these are the current offers at Mtgox:
http://bitcoincharts.com/markets/mtgoxUSD_depth.html