Just because you're drawing a cartoon version of your zombie, doesn't mean you should forget your anatomy and do a rush job. Take your time. Practice anatomy. This is very important for regular human characters and zombies so keep practicing and more importantly: Have fun!
Sketch out a proportional image of the zombies body. Use circles and blocks to detail the body parts and joints. The head is a circle, the torso a block and so on. This can help a lot when coming up with different poses for your zombie.
Go back and add detail to the face of your zombie. Decaying skin, exposed brain, and loose eyeballs are a good way to add effect.
Next sketch out the clothes. Remember to tatter and rip them as much as possible. There is no limit to how large the gapes can be. Don't forget to keep the edges tattered and worn.
Detailing the body. Anywhere you can make your zombie look dead is good. A few key areas to pay attention to are the hands and legs. Remove a few fingers, but the ones you keep emphasize the long overgrown dirty fingernails. Zombies have never been known for their cleanliness. As for the legs I remind you the more tattered the clothes, the better. Also, zombies are forgetful. So if your zombie lost his shoe somewhere it may make him seem a bit more believable.
Ink. Take. Your. Time. Make sure to get every detail. Wrinkled skin, tattered clothes, and decaying flesh are the main parts of a zombie! So don't over look them during this crucial step.
As you colour your cartoon zombie don't forget blood splatters always help set the mood.
Remember: Practice makes perfect and HAVE FUN!