1. The shadow is primarily a darker version of the local color of the surrounding area. So, if you have green grass in shadow, the green will be darker than the grass in light. (This is pretty obvious, eh?)
2. Skylight bounces down into shadow areas. If the sky is blue, some of the blue will show up in the shadows - especially the outer reaches of the shadow that are farthest away from the object casting the shadow. (We've all heard about putting blue in shadows.)
3. Thanks to "simultaneous contrast," a bit of the complement of the surrounding illuminated color will show up, too. Taking the grass example, since grass is green, you'll see a little red in the shadows. (Now we're diving into an esoteric area...)
4. Finally, whatever the hue of the light source is, a bit of it will bounce into the shadows. So, if there's a yellow sun, a bit of the yellow will be there, too, thanks to halation. (Huh?)
Sure, you can think about all these effects and try to weigh which of the four dominates a particular situation. But here's an easy solution - observe closely and paint what you observe. It's that easy!
In the following sketch, I focussed on capturing the effects of bounced light in the shadow area. I've kept to a minimal my involvement with shape and design.
5x7, pastel