Here's an example of what I'm referring to. I've been noticing a couple examples of meshes like this in low poly stuff lately, but I don't know how I would end up doing something similar? I'm specifically referring to the circular parts like the belly and eyes - IDK what the mesh would end up looking like.
When I model little things like this, I've been starting from object primitives similar to the shape I want, so my meshes are more grid-like.. If I were to try to color the belly a different color, it'd be a rectangle. I did try projecting a plane for the ears i n this example, but I think I'm doing something wrong. Is my problem that I'm only doing box modeling, and not polygonal modeling?
You would do well learning on the mesh modeling bootcamp courses here on CGCookie and learning about topology. It will serve you well.