The answer
The train station is underneath the terminal — €5.20–6.20, 17 minutes to Amsterdam Centraal. Just tap your contactless bank card or phone at the yellow posts (OVpay). No ticket to buy, nothing to queue for.
Trains run every few minutes by day, hourly through the night. It's the default move for almost everyone.
Staying near the Museumplein or Leidseplein? Bus 397 (Airport Express) — €6.50, card only, drops you in the museum district without the Centraal detour.
⚠️ The traps (walk past these)
The inside-the-terminal taxi touts
Schiphol has a persistent problem with men in the arrivals hall offering "taxi, cheap price" — these rides routinely end at €100–150 with intimidation at the destination. It's enough of a problem that the airport runs warnings about it.
Do this: official rank outside Schiphol Plaza, or book Uber to the app pickup zone. Nobody legitimate asks you first.
The I amsterdam card gap
The I amsterdam City Card does NOT cover the airport train or bus 397. Tourists buy it at the airport expecting the ride in to be included, then pay the fare anyway.
Do this: just tap your bank card for the airport leg; buy city passes later if you actually want one.
The paper-ticket surcharge
Buying a disposable paper train ticket at the machine adds a surcharge over the contactless tap price, and queues at the machines after a widebody lands are grim.
Do this: walk past the machines, tap your card/phone at the yellow post, board. Tap out at Centraal.
Forgetting to tap out
OVpay charges an incomplete-journey fee if you don't tap out at your destination. First-timers tap in fine, then follow the crowd straight out of Centraal.
Do this: tap in AND tap out with the same card or phone. Same device, same card — switching mid-journey double-charges you.