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.
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.
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.
Avoid splicing motor power cables when ever possible. Ideally, motor power cables should run continuous between the drive and motor terminals. The most common reason for splicing is to incorporate high-flex cable for continuous flexing applications.