How can I use PWM to power a 1.5v dc motor with an 5v board Arduino UNO?
Firstly, the Arduino microcontroller is not suited to driving any motor directly. See the comments for a discussion of suitable solutions, including H-bridge drivers. Motor shields are widely available for Arduino Uno controllers.

Secondly, I have checked the Arduino reference for AnalogWrite and it appears this function is not available for pin 13 on the Arduino Uno which you mentioned you are trying to use.


  On most Arduino boards (those with the ATmega168 or ATmega328P), this
  function works on pins 3, 5, 6, 9, 10, and 11. On the Arduino Mega, it
  works on pins 2 - 13 and 44 - 46. Older Arduino boards with an ATmega8
  only support analogWrite() on pins 9, 10, and 11.


Finally, if you would like to use this motor then you should check the datasheet. The motor is rated for a nominal voltage of 1.2 V and a no load current of 0.2 A (200 mA). Under load or stalled, the motor will draw more current.