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.
Magnetically soft materials, however, tend to be more expensive. The motor manufacturer must find that proper blend of just enough magnetically soft material to do the work required without putting too big a dent in the customer wallet.
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.
The colors or numbers themselves are often a clue, but they alone may not provide sufficient information. There is always the trial and error method, but I do not recommend that because of the potential for destructive results. Instead, the Motor Doctors suggestion is to equip yourself with an ohmeter (don nott settle for just a continuity tester) and learn to perform a few simple tests with it.