The train station in the airport of Amsterdam is almost directly after where you leave the customs area. You do not have to leave the airport building to buy train tickets or go to the train platform (the Schiphol train station is underground).

Trains between Schiphol go day and night (night service is once per hour). In the daytime, there are up to 6 trains per hour to Amsterdam Centraal.
Trains take about 20 minutes to Amsterdam Centraal, and travel via stations Amsterdam Lelylaan (trains do not always stop here) and Amsterdam Sloterdijk (trains always stop here).
A single ride to Amsterdam Centraal is E 4,20 (price level 2016).

This train station can easily be reached from within the airport building. After leaving the plane it is just a few minutes' walk.

TIP 1: Beware of pickpockets on this line. Always keep a close eye on your belongings..
TIP 2: On the line Schiphol - Amsterdam there are frequently (technical) failures and delays. You can check this beforehand on the railways website (ns.nl). The NS app also has this information. It is advisable to take your time for the trip.