Hi Susan,
Most people think there is some magic way to decorate products, but the fact is, decoration like you described is actually done by hand in most cases. Figures have to be hand painted simply because we have not invented machines that can do it. In the case of printing decoration many times that’s done with pad printing, or other techniques.
I’m not sure if Stephen has any over there, but there is a section here on manufacturing, and Stephen puts videos up on the different techniques. You may ask him to post some things on “Pad Printing” and “In-Mold Decorating” ….both are popular ways to decorate products.