The key to making any photo or illustration look realistic is creating realistic lighting. That means you have to know what your light sources are and where they’re coming from — even if they’re not in the picture.
Using that same technique — imagining the light source in your image — now think about which areas would be cast into darkness. In this example, since you’re visualizing the sun at the top left, as a general rule of thumb you’d want to add a line of shadow to the bottom right of each object.
Remember, your shadows don’t have to be straight lines that follow the outlines of your illustration exactly. Fill in entire areas that would be darker, like the shadow a chin creates on a neck, hair creates on a face, or eyebrows create on eyelids. Think about which objects would create larger sections of shadow for nonhuman subjects, too.