How do I make the Ardumoto shield work properly?
Your best bet is to drive the tiny motor directly with a darlington transistor like the BC517 and 5V, or make 6V and drive it off that. The motor shield is simply overkill for this. Just make sure you dont stall it - the shortcut current in this setup might be to high. Do not forget to add a flyback diode antiparallel with the motor in this setup.

You might put a resistor in series with the motor. 

A voltage divider in front of the motor will not work, because the lower part of it is parallel to the shield or motor.