How I shade in adobe Illustrator isn’t as straight forward as in Photoshop. In Photoshop you grab a brush, or the burn tool and your mostly set to go.
When your live paint is expanded you need to select the color surface you wish to shade with the direct selection tool.
To create soft shadows add a gradient effect to the selected area. When you add it the gradient window will open automatically. If it doesn’t navigate to (window/gradient).
You need to mess around with the gradient settings a bit to achieve your desired effect. You can make the gradient circular, linear or mirrored if you wish. The point is to create a soft shadow gradient. We’ll be adding the harder shadows later on.
You can also adjust the point at which the gradient starts to blend or how long it blends. You do this by moving around the diamonds at the top of the gradient indicator.
After the gradient is applied duplicate the surface you want to shadow (just copy and paste it in place with cmd/ctr+shift+v). Keep the new surface selected. If it’s not, select it with the direct selection tool.
Select the knife tool. We are going to create the hard shadows now. With the specific colored area still selected start slicing along where you want the dark shadow to run.
Make sure you slice the object from one end to the other, not leaving any gaps. What you are doing is basically splitting the surface in to the shadowed part and the light part.
Now deselect all the parts intended to be shadows one by one with the direct selection tool and shift clicking on them. Delete what’s left selected. All that remains are the parts intended to be hard shadows.
Select those parts and apply the desired color of shadow to finish your illustration.
Conversley you could also use the patfinder tool to create the hard shadow surfaces. It’s more precise but you will use up more time. You can read up on the pathfinder tool in this article.