If you are using a PWM signal to drive the LED's, you will need possibly a MOSFET system. If you get an NPN, You would connect the base of the MOSFET to the output pin of the arduino via a resistor(value unsure at this point but will vary with the choice of mosfet) the collector to GND and the emitter to the anode of the LED(s). you also need to link the GND of the Arduino to the GND of the plugpack. Can anyone verify my logic here? Also I think you would benefit from a voltage regulator too.
MOSFETs don't have base, emitter, and collector leads. They have gate/source/drain leads. If you use a mosfet be sure it's a logic level mosfet. The connections told above are for a NPN bipolar
transistor. A TIP120 is a nice cheap darlington NPN transistor that is great for switching things on or off or PWM from an Arduino output pin.