See attached - motor drive using a MOSFET. Resistor from arduino pin prevents pin from being damaged by inherent gate capacitante.
Resistor to ground keep MOSFET off during reset when IO pins are defaulted to Input until sketch starts up.
MOSFET can be an NPN transistor as well; resistor to ground is not needed.
power supply ground must connect to arduino ground for common reference point.
PWM from whatever pin limits motor current by rapidly turning on/off at ~490 Hz, amount of High time (0 = off, 255 = full on) determines how fast motor will spin.
