What subway to take from Amsterdam airport to nearest downtown center?

There is no subway. Take the train to City Center. The station is under the airport.

The easiest way is by train directly from the airport to Amsterdam Centraal Station. It costs €3.80 and takes about 15 mins normally. It is far cheaper than a taxi, safe reliable and they leave (approx) every 10 mins from the platform right inside the airport. You can also buy your ticket from the nearby booths or yellow automated machines (in English as well), so you can’t go wrong!

For more details you can see it online (timetable, prices etc)
http://www.ns.nl/servlet/Satellite?cid=1075985690180&pagename=www.ns.nl%2FP age%2FSuperHomepageEnglish&lang=en&c=Page

As already pointed out, the NS railways train leaves from directly under the airport to Amsterdam Central station which is in the heart of the city. I bought my ticket with a credit card at the automated ticket machine in the arrivals lounge near baggage claim.

Have fun. Amsterdam rocks !

Schiphol lies between several citiies. Amsterdam, the Hague, Leiden, Haarlem, Hoofddorp, Utrecht. Amsterdam and Haarlem are closest.
Take the train. (train goes night and day)
You could use cheaper train tickets if you have train pass for travelers, railplus.