blower only operates while turned on full, it does not operate on lower speeds

What is the best way to diagnose the blower switch in this case

on the resistor, you should have a ground wire and either three or four wires that are your speeds from the switch. with a voltmeter, you should be able to see changes in which wire has power; which would indicate if the switch is okay. usually, if you only have high speed and that's all, it is the resistor.