Create a corporeal outline of your character. What physical traits would she posses? How tall is she, how old? What color is her eyes, her hair, her skin? These outlines are far more important for television characters than book characters, because a physical actor must play the character. It cannot be imagined by the reader, like with book characters.
Create a personality outline for your character. Put on paper a general overview of his temperament, emotional traits, work ethic, and methods of communication with others. Make sure your character doesn't come off as too perfect, some flaws make them relatable and interesting.
Create a history, where your character's from, what was her childhood like, and how did she end up where she is now? Character histories often come up on TV in the form of flashbacks or stories, so it's a good idea to have a few specific memories written out for future use.
Create a setting. Where does your character live? In the city, the suburbs, perhaps somewhere more interesting, like a cruise ship? Who does he interact with every day? How did he end up where he is?
Make a plot line for your character, even if it is loose. A general idea of the stage in life she's at, as well as personal goals. Keep in mind that your character's path will be intertwined completely with the plot of the television show, so a set story may not always work.