Orders and "fills" are confusing! Back around the small panic during mid April, I tried to sell a large qty of XBT to USD quickly on an exchange. I expected that I would get current USD/XBT quoted on that website times # of XBT in my account. I was very wrong.

Instead, the exchange broke my transaction into several smaller transactions of various sizes, sold some quickly while others took as long as 30 minutes to convert to USD, and none of these sub transactions were converted at the price quoted on the site.

As I understand, that's because every exchange has Buyers and Sellers whose Orders are like virtual post-it notes on a bulletin board announcing their desire to buy or sell A amount of currency at P price, and the exchange just tries to "find good matches".

Is that true? And is it true that every exchange has its own algorithm for doing so and there is no "standard" for how such an algorithm should operate? If so, what info do I have to go on if I want to have a good idea of how much USD I will get for my XBT when I place a Sell order at Exchange X?
That is how most exchanges work, with an order book containing bids (buy) and asks (sell) orders. The trading engine of the exchange will match orders as quickly as possible, though in cases of a crash or excessive volume exchanges have been known to suffer a severe amount of trade lag (e.g. mtgox), resulting in orders not being filled at the last price when submitting an order.

Here's an example of how an exchange works:

You have 1 XBT you would like to sell for $1000, so you go to an exchange, deposit your coin and place a sell order of 1 XBT @ $1000. If there are bids over $1000, your order will fill at the price of that bid. E.g. If there is an order to buy 1 XBT @ $1050, you will receive $1050 less exchange and withdraw fees.

If there are no buy orders above $1000, the exchange will put your order in the orderbook and wait until it fills or is cancelled (or expires, in some cases on some exchanges). In this example, if someone were to later place a bid to buy 1 XBT @ $1050, they will pay $1000 for your order (providing there are no orders trying to sell XBT for less already on the book).

If you are trying to sell in an easier manner, I would recommend using Coinbase, which works very nicely within the US.