From Schipol Airport, follow the signs to the Arrival Hall. You'll go through customs and then spill out into the main airport area. Here you'll find escalators down to the train platforms and electronic kiosks for buying tickets. We don't have a PIN for our credit card so could not use the kiosks. The live ticket agent said travelers will be required to use the kiosks after February 2009. Our tickets were 4 .50 euros a person. A Holland travel planner and interactive kiosk demo is available here.
There is only one platform with two tracks. The trains to Amsterdam run on both tracks. Getting luggage down to the train via the escalators is no problem but getting big luggage up on the train could be a struggle.
The ride to Amsterdam's Central Station takes about 15 minutes. Trams are available in front of the station. Walking from the train to Dam Square takes about 10 minutes.
From Dam Square, Vondel Park is about another 20 minutes on foot. You can walk anywhere in the city in a half hour or less. We never used the trams. Too cheap and already packing extra carbs.