Take the train to station Bussum-Naarden, then take the bus to Amsterdam and stop in Naarden Vesting. You can also walk, it's not that far, 2 km at the most. Only make sure you take the right path. I took what I believed was a shortcut but what definitely wasn't, and I was exhausted when I finally arrived in the town.
Naarden is being served by Connexxion busses:
-110 to the Weesp and Bussum train stations
-151 to Almere Haven