The trainstation of Amsterdam Schiphol Airport can be found right under the airport’s central hall. This central hall is in walking distance of all arrival halls, so you don’t need an shuttle bus or other transport. Almost every 10 minutes, a train runs from Amsterdam Schiphol Airport to Amsterdam central station. This takes around 20 minutes, and costs €4.20. There are several yellow machines where tickets can be bought. Tickets can also be paid at the counter of NS Dutch Railways, but a this will add and extra euro to the ticket price.
You can also buy an Amsterdam Travel Ticket, which includes a return ticket from the airport (not valid on the international train Thalys) and unlimited transport with buses, trams, metros, and ferries in Amsterdam. The card costs €15 for 1 day, €20 for 2 days, and €25 for 3 days. You can buy this ticket at the airport at the NS Tickets & Service counter, or at the AKO stores.
There are local buses that stop right in front of the airport. This might be convenient if you are staying somewhere close to the airport, but outside of Amsterdam. If you are staying in Amsterdam it is usually quicker to take the train. However, bus #197 stops at Schiphol, Museumplein, Rijksmuseum, and Leidseplein, and might be more convenient if you are staying in those areas. You can be ticket online (through their website) for a reduced fee of €4,75 for one-way and €9 for a return ticket. If bought from the driver, the costs will be €5 for a one-way ticket. The bus departs from a busstop in front of Schiphol’s main hall every 15 minutes during the day and once an hour during the night. The trip will take around 40 minutes.
The Amsterdam Travel Ticket (see above) is also valid on this bus.