Public transport
Amsterdam has a rather confusing array of public transport: busses, trams, and the underground. Study the map carefully to look for the quickest way to reach your desired destination. In march 1997 a new line was introduced: tram 20 a.k.a. the circle tram. On its route are all the main sights and museums. It's quite popular with the pickpockets too.
Amsterdam is divided into twelve zones. You have to buy a OV Chipkaart to ride on the buses, trams and mediocre subway.
A few years ago, riding trams and the underground without a ticket was immensely popular among the locals. However, control has been increased and you have to pay a hefty fine if you get caught.
Dutch Railways (Nederlandse Spoorwegen, NS for short) has a rather good site: http://www.ns.nl