Here's a quick recap of the method:
The first thing I do is prepare my palette. I have a specific order as to where I put the colors. The subject will dictate the final selection of the colors, meaning I may add a color that I don't normally use, such as cobalt blue for clouds or a sky, but I have a standard palette of 12 colors. I added manganese violet a few years ago when I discovered it was green's perfect complimentary color for landscape painting. It essentially turns the chroma or intensity of the color down a few notches.
Here's my palette: From left to right, Titanium Everwhite, French Ultramarine Blue, Cerulean Blue, Viridian Green, Manganese Violet, Alizarine Crimson, Cadmium Red Light, Cadmium Yellow Barium Medium, Cadmium Barium Orange Medium, Burnt Sienna, Yellow Ochre and Burnt Umber.
Notice, there's no black on my palette. After I discovered I could mix a deep, rich black from burnt umber and ultramarine blue, a la Anders Zorn, I went cold turkey and removed black and all its variations from my palette. A student once asked me what I had against black. I had to think about that for a minute. I don't like black because it seems so one-dimensional. By that I mean it's a neutral black. By mixing different amounts of ultramarine blue and burnt umber, you can tweek the temperature. More blue will make it cooler, more umber will make it warmer. You can make lighter versions of black (I think it's called gray) by combining cerulean blue or burnt sienna or any variation of blue and brown. I know Sargent had black on his palette. After a steady diet of looking at Munnings' paintings for a few years with his bright colors, I was alarmed to see how much black was in Sargent's flesh tones!