Schiphol train station is located right underneath the airport (which is handy) and is clearly signposted when you leave Arrivals. From here, the Dutch National Rail service, "Nederlandse Spoorwegen", (NS) runs train services that take you directly to Amsterdam Central Station in around 25 mins.
Around 5 trains an hour run from the airport to Amsterdam Central station throughout the day. At night, from 1am to 4am, the trains are once an hour and run from Utrecht CS to Amsterdam CS - Schiphol Airport - Leiden CS - The Hague CS - Delft and Rotterdam CS and back, not stopping at smaller stations in between (CS stands for Central Station, in case you were wondering).
You can buy train tickets from the ticket office in the main hall of the station or from yellow ticket machines near Baggage Claim, in Schiphol Plaza shopping centre and on the station platforms. The machines accept cash, debit and credit cards and, rather nicely, it's cheaper to buy your tickets from them than from the ticket office. For more information visit www.ns.nl.
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