Upon arriving Amsterdam airport, we need a train to Bruges. By purchasing the tickets at the airport, does one have to pay in cash (Euro's) or can they be paid for by credit card? Also, what are the fare costs for a one way, and where are there train changes? This travel will be in late October 2012.
Dutch Rail only accepts chip & pin cards at both the ticket counter and the machines. So you'll have to pay with cash for the regular intercity trains. If you want to travel via the high-speed Thalys train you save money by purchasing in advance via the website but you will be locked into a specific departure. Check schedules and purchase web tickets here: http://www.nshispeed.nl/en
To answer your other question, you change trains in Antwerp. As implied by the other poster, you can opt for either the high-speed Thalys service, or a marginally slower intercity train. Thalys ticketing and pricing work much like airlines. The earlier you purchase a ticket, the cheaper, and your non-transferable ticket buys a specific seat on a specific train at a specific time. Thalys does not regularly service Brugge, so the second leg of your trip will be on a normal Belgian rail intercity train. I do not believe there are any advanced discounts for the intercity train, and reservations are not offered. Unlike Thalys, your ticket does not lock you into taking a specific train. Because the second leg of the trip between Antwerp and Brugge will be on a regular intercity train, you are also not locked into any specific connection. You can grab the next train to Brugge, if you wish, or you can walk around Antwerp for a few hours and catch a connecting train at your leisure.