Stop at a train ticket window and buy a one-way ticket to Alkmaar. The price is about 15 guilder per ticket. Trains leave for Amsterdam from the airport every 20 minutes starting at about 5 AM, less often in the small hours of the night. If you happen to catch a train that stops at Amsterdam-Sloterdijk , on the west edge of Amsterdam, change there, go to platforms 1 and 2 on the lower level of the station, and catch the train to Alkmaar. It's just over a half-hour ride from Central Station.
Most Dutch people speak English.
If you get confused, ask for help from anyone at hand. In two minutes you'll be at a light on a T intersection. Go to the left along Scharlo. Walk on 200 meters or so to the bridge, the Bergerbrug. This takes you across the Singel, the canal that surrounds the old town.