First of all, what is a Grisaille underpainting? It is actually very simple. Grisaille underpaintings are monochromatic underpaintings, usually done with Raw Umber and white, to create the tonal composition of your painting. The reason Raw Umber is used instead of Ivory Black is because it has less oil and dries very quickly (mixed with Gamsol, it can take less than a day before being dry to the touch).
So why would you use a grisaille instead of just directly painting? I use it to establish my lights and darks early in the painting. It is much easier to get your colors correct once you know where your lights and darks will be situated in the painting.
Once the picture is drawn in vine charcoal, I mix my 4 main tones (2 lights and 2 darks) for the painting with Raw Umber and Flake White Replacement. Both paints contain very little oil and will less likely crack with more layers of paint added later (fat over lean). The White Replacement does take a few extra days to dry, but I like to use it to create a little texture (especially when mixed with some Cold Wax).
The book that really got me into grisaille underpaintings was Solomon J. Solomon’s- The Practice of Oil Painting and Drawing. Grisaille underpaintings have been used for centuries from painters such as Titian, Rembrandt, Rubens, Van Dyke, and Velazquez just to name a few. I strongly recommend trying this technique if you want to create balanced tones in your paintings.