Write a strong story premise that will drive your cartoon series characters. One or two sentences tops. For example: "An alien baby with superhuman strength crash lands on Earth and is adopted by a human family." It's this simple yet strong premise that drives "Superman"
Sketch your main character first. If it's a series team like Ren and Stimpy, draw both first, preferably on the same page. As you draw, keep the story premise in mind.
Write a brief description of your main character or main character team. No more than two sentences per character. For example: "Popeye is a weak, scrawny, one-eyed sailor who gains superhuman strength after he eats his spinach."
Sketch your main character or main character team again with the brief written description in mind.
Start drawing more characters. These characters should spring from your main character or main character team. Draw a villain or nemesis. Draw a love interest. Draw a sidekick.
Draw all your cartoon characters in a grouping that might resemble the front-view of a jailhouse lineup. This grouping will give you a strong idea how the characters relate to each other physically and perhaps attitudinally.