Choose a race for your character. In the "Invader Zim" universe, most characters are either aliens, robots or humans, with the primary alien race being Irken.
Come up with a motive for your character that fits into the "Invader Zim" storyline. Irken characters in the "Invader Zim" universe are motivated by their involvement in Operation Impending Doom II, the mission that sent Zim to destroy Earth. Human characters are either attempting to stop Zim or trying to accomplish their own goals, most of which revolve around the high school where Zim and Dib are enrolled.
Design your character's physical traits. Irken aliens are usually in "human" disguise when on Earth, so you'll need two sets of physical traits for an Irken character. Human characters are mostly either adults or teenagers, with adults towering over smaller characters in an exaggerated manner. Clothing design is simple and dynamic---study the animation style of Invader Zim to get a feel for the typical character design.
Name your character. Most character names in the "Invader Zim" universe are single-syllable nonsense words, such as Gaz, Zim, Dib, Gir and Tak. You can follow the consonant-vowel-consonant pattern to come up with a good character name that sounds appropriate for the "Invader Zim" universe.
Create a character sheet with your character's personality, appearance, motive and name. You can draw a sketch of your character in the style of "Invader Zim" to use as a reference as well.