Bitcoin currency exchanges work in a manner similar to banks. One first deposits amounts of money in the currencies supported by the exchange, to his own account in the exchange, uses these balances to trade with other users of the exchange and then withdraws that money. Unlike over-the-counter transactions, there is no risk of losing money due to people not fulfilling their part of the deal, as long as the exchange itself does not commit fraud or withhold money.
Exchanging is done by placing “buy” or “sell” orders, which the exchange system software then matches with each other. “Buy” orders (or “bids”) are offers to buy bitcoins in exchange for another currency at a maximum price-per-bitcoin which is set by the offerer. “Sell” orders (or “asks”) are offers to sell bitcoins at a minimum price-per-bitcoin. If the bid price of a buy order is higher than the ask price of a sell order, an exchange can be performed and either the bid order, the sell order or both can be removed from the “order book”. Thus, at any given time, there is a price above which there are no more buy orders and a slightly higher price below which there are no more sell orders.
Communication with the Bitcoin currency exchanges is commonly done using a standard web browser, over a secure SSL connection.