Amsterdam is laid out in concentric semi circular rings of canals, with roads and bridges running from the center over these canals towards the outer edges.
The most northerly place that most tourists will venture is Centraal Station, Amsterdam's main railway station. Most visitors will start their tour of the city here, as the train from the airport and trains heading to other European cities generally start and end their journey here.
Almost all attractions lie south of Centraal Station. About half a mile south of Centraal Station is Dam Square which is generally taken to be the center of the city. Here you can find a number of attractions such as the Koninklijk Paleis, Nieuwe Kerk and Madame Tussauds. When standing on Dam Square, you are basically in the middle of the canal rings which surround the city.
Directly to the east of the square is the Red Light District called de Wallen. This is one of the busiest nightlife areas in Amsterdam. Another popular place to head at night is Leidseplein, which is south west of Dam Square. Here you can also find attractions such as the Van Gogh Museum and the Rijksmuseum.
Another popular area is Waterlooplein which lies to the south east of Dam Square. Near this square you can find the Muziek Theater, Artis Zoo and the Joods Historisch Museum. Waterlooplein is also good for shopping with daily markets held in this area, as well as for nightlife.
The center of Amsterdam is not particularly spread out, and indeed most interesting points of interest can normally be reached on foot. However if you're getting a bit tired, water taxis and trams run along an perpendicular to the canals, making it fairly easy to get around.