Here the short answer :
A character designer is a traditional artist who creates original drawings of characters for the visual media. The character designer goal is to create characters that fulfill the needs of scripts,scene,game and story.
Where to begin :
Imagine you are a character designer who's been hired to work on a feature film for a major animation studio. The directors of the film ( there always seen to be at least two for some reason ) have introduced themselves and have pitched the general idea of the film. In a pitch, the directors simply tell the story to you usually with the aid of plenty of drawings and character designs.
Imagining the characters:
Your first task is just to sit and think.