Without getting into a lengthy physics lecture, this process of reversing polarity produces heat (or wasted energy). This is known as hysteresis loss. And that helps explain why increasing the voltage into the motor will not necessarily increase the output. Instead, it can fight the resistance of magnetic materials to reverse polarity--and simply heat iron.
As a technician, I naturally look at things from a nuts & bolts perspective. As technicians, we understand objects and assemblies. We understand how things come apart and go back together. Is not this what Einstein and Ohm did? They figured out how "it" comes apart, which led to the ability of others to put "it" back together.
You will need to use the ohmmeter as an ohmeter and not as a continuity checker for the next step in the procedure. You will want to use the lowest ohm scale your meter offers, as the typical winding resistance in motors such as these is less than 100 ohms. If the motor is a permanent split-capacitor motor, you are going to be looking for common and speed taps of the winding.
Wiring diagrams happen to be a perfect vehicle for carrying the principles of technicians beyond nuts & bolts. First, the simple act of color-coding helps to bring out the true wealth of your knowledge and is an excellent step in diagram analysis. Beyond that, it is an amazing tool for developing the awareness needed to get on the road to becoming an expert learner.