The quickest way to get to the Zaanse Schans from Amsterdam on public transport is by train. From Amsterdam Centraal, catch the sprinter train towards Uitgeest. In about 17 minutes it will get you to the station Zaandijk Zaanse Schans, where you get off. For more information on the train, head to the official Nederlandse Spoorwegen railservice website. From here you either get to the entrance of the Zaanse Schans neighborhood by foot, which is about a 1-kilometre (12-minute) walk. Or alternatively you can rent a bike near the train stop (on Google Maps: FR94+JC Koog aan de Zaan, Niederlande) and do the rest of the trip by bike.
Alternatively, there is a bus (busline Nr. 391) that runs directly from Amsterdam Centraal towards the Zaans Schans. This will take a little longer as the bus takes about 45-minutes for the route, however it will save you the 1-kilometre walk/bike ride if you are not into that.
You can also get there by car, but I would not necessarily recommend renting a car in Amsterdam just to go to the Zaanse Schans. If however you are doing the Zaanse Schans as part of a Netherlands roadtrip, there is a parking lot next to the Zaans Museum. Just be aware that it is quite expensive to park here (between 11 -15€ depending on the season).