Buy yourself a DVM (digital volt meter). They can be had for about $10 these days although you can spend a lot more. Auto parts stores usually have them although they will probably be a bit more but you should be able to find one for $20 or less.
With a meter, it's pretty easy to trouble shoot a lot of electrical issues. In this particular case, you would set the meter to the appropriate setting by moving the dial on front (it will probably have a 20V max DC setting, which is fine for car work) and then put the meter probe tips on the 2 wires supplying power to the wiper motor. Turn the wiper switch to turn the motor on and see if the voltage is a constant 12V or not.
Another way to test the motor would be to just supply 12V to the wires to see if the motor runs normally or not. However, you will need either a power supply or some jumper wires to connect to a 12V battery. I have all that stuff around the house - somewhere - but if it was me, I would probably just order the part on ebay too since a) it's easy and b) I think the odds are good that the problem lies there.