First, you'll need to think about why Zombies walk the way they do. Like any good actor, you'll want to get into character.
You'll want to think about what your Zombie is seeking. It could be a good-old-fashioned craving for human brains or the more sinister world domination? Like people, all Zombies are different. Some Zombies are looking eat a whole person, others just want brains.
Before you start walking, think hard about what your Zombie will be seeking. If it's brains, for example, you're Zombie most likely will have his arms raised up perpendicular to your body to better reach those brains. If it's a heart, maybe you'll want to point those arms a little lower. But if it's the entire body of the victim that the Zombie wants -- like in, say, "28 Hours Later" -- your Zombie is probably going to move those hands a lot when walking.
In the newer Zombie flicks, like "Zombieland", the Zombies have adapted a higher mobility than in the original George A. Romero films. The original Zombies pulled themselves out of they're six-feet-under coffins after years of being dead. They were, to say the least, slow.
Start with this idea: You're legs probably would be pretty stiff if you had been lying in a coffin for a few years. So don't, under any circumstances, bend you knees. (Go ahead, try it!) And then, once that no-knee walk has been mastered, go ahead and cut out the use of your ankles. It's not easy, but it will help your credibility. Turning your toes in like a duck and dragging your feet will help tremendously.
Zombies don't seem to change their minds much, so your Zombie walk should be in a straight line toward your goal. Keep your hips loose, but don't add to much side-to-side motion, or it will seem like you're part of some undead Congo line.
Zombies in most flicks tend to take their time. You'll want both feet on the ground as much as possible -- taking short, listless steps. Don't get too animated, or you'll quickly seem more alive than undead. (That's a huge distinction.)
So, now you have passed Zombie 101 and you're an expert in walking like Zombie. What do you want to do with your skills? You could just practice in your apartment for a few months, showing them off to your cat. But this might be better: Join the masses at one of the organized "Zombie Walks" around the world.
In San Diego in July, there's an annual Zombie Walk that coincides with the Comic Con convention. In Montreal, the annual Zombie Walk takes place in August.
If you have seen a Zombie movie lately, you know that while one Zombie is scary, a street full of Zombies is terrifying.