You should be able to isolate into two groups any leads which have continuity with one another. The starting circuit is likely to isolate to two leads, the running circuit may have two or more leads that show continuity. If the running circuit has more than two leads, you will need to determine how those leads are to be used for voltage or speed changes.
Now we have better ideas about how electricity works, we tend to talk about current as a flow of electrons, from negative to positive, in the opposite direction to the conventional current. When you are trying to figure out the rotation of a motor or a generator, be sure to remember that current means conventional current and not electron flow.
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.
The power of simple is manifested in that others were able to build from the foundation Einstein identified and defined. They were able to accomplish things they most likely could not have otherwise. We also have experienced this phenomenon. Consider Ohm law. Georg Ohm did the hard work and broke down the complex to a simple law. We use the principles contained in that law as a starting point to understand the complexities of electricity and circuit dynamics.