Character design is a very unique and very hard department to get into. Cause it's all about design, there's no fancy painting technique to cover it up. Most of the best Character Designer knows how to animate and a great observer of people and personality.
I'm very lucky to have been given character design assignment at DWA. I learned everything I know from Tony Siruno. He is one of the best character designer I know. His design is cool, refreshing, and effortless; which is a really hard thing to master. And he is also a really good teacher, very patient and very generous with his knowledge.
This is one of the way Tony taught me to approach character. I'm using Grug as an example, (a character from the Croods).
1. Inspiration page
This is the idea in general, of course there's more to it within the design itself. But this is a good place to start.
Try it out and have fun,