The distance between Schiphol Airport and the Central Amsterdam is approximately 15 km (9 miles).
The cheapest way to get from Schiphol Airport to Amsterdam is by train.
The train station is located underneath the airport and trains depart every 10-15 minutes to Amsterdam Central Station. The one-way ticket costs €3.80.
Don't buy a return ticket unless you will be coming back to the airport the same day, tickets are only valid for the same day.
You can choose between Fist Class or Second Class tickets.
However, if you want to get to your hotel directly from the airport the best way to do it is by bus:
-The KLM Shuttle will get you directly to 15 major hotels in the city for €10.50 one way ticket. Notice that it is not necessary to fly with KLM to make use of this bus service.
-The Conexxion Schiphol Hotel Shuttle operates between 6.00 a.m. to 21.00 p.m. from Schiphol Airport to more than 100 hotels in the city. For more info about this service and prices please check this link.
If you want to find out more about Schiphol Airport Public Transport please see this link.