Any avid Dragon Ball Z fan might conjure up the idea for a new character when seeing the depth and originality already present in the cast list of the international phenomenon. You might use this new character to write a fan fiction or simply as inspiration for something to draw in your free time, but regardless of use, there's no denying that creating a Dragon Ball Z character is an exercise in creativity.
Decide where the character's affiliation lie, he might be a "good guy", one of the entourage consisting of the heroic Goku, Gohan, Gotenks, Piccolo, Tien, and Yamcha; or a "bad guy", such as one of the Androids.
There are tertiary characters as well, who don't actively fight for either side. With the depth and variety of the cast, you can create the "secret brother whose been hiding his whole life" of almost any character in the series, so the possibilities are endless. For the sake of ease, assume the character is a male, although you can choose to design a female character for any of these situations as well.
Find where the character fits in the family tree. Most characters in DBZ are related to someone, and your character probably is too. A Dragon Ball Z family tree (See Resources) will be incredibly crucial to this part of the process.
Create a backstory. Everyone has a backstory, even if they don't share it. Whether you plan on using the character to write fan fiction or just to have a character that you came up with yourself, the story of your character's life has a lot of influence on his actions.
Place him in a situation and let the character create itself through its actions. Make him challenge Android 19 to a fight and see who would win, or have him build a castle in Buu's honour. The more you write about him doing, the more the character begins to create itself.
Come up with a sketch or basic idea of how he looks so you can describe him. This grounds the character in realism and breathes life to your idea.
Write stories about the character; this is the most common use. A lot of forums exist for you to share your Fan Fiction (See Resources). Otherwise, feel proud about your accomplishment and keep coming up with ideas for characters.
Put away an hour or so to fill out your character through these steps, you can't rush the process of character creation.
Make sure your character's existence is plausible--i.e., don't say he's the son of two people who would obviously never get together. Or do it if you want to, just remember that people who you tell about your character might be overly critical. At the end of the day, it's your character to do with what you please.