It's great to see articles this this appearing in the beauty industry. I am a colour analyst teacher, and just recently trained as a nail technichian. I know it is so, so important to get your colours right (or wrong if you want to create a clashing, high fashion effect - understanding colour can help you do this).
In the beginning of my course, I give my students tubes of the primaries in watercolour, and get them mixing to make secondaries, tertaries and complimentaries, and then progress to tinting and shading them. I recommend you could try this to help you understand this tutorial better, then you can start practicing with your products.
I agree with the comment that clashing tones will make the enhancements look as if they're growing out in 5 minutes, this is so true, the same goes for the wrong make-up tones, clashing tones will just not look right. A cool skinned person wearing warm make-up will look bland, and a warm-skinned person wearing cool tones will find the cosmetics 'sitting' on the face, looking harsh and tarty (if you're 19, skinny and georgeous you may get off with this, but for anyone else, it looks bad, and the more mature your client is, the worse it looks). It really pays to know this stuff, it can make a real difference to your business.