How do zombies move if they aren't living?

Other than the fact that they are not real and don't move at all except in the mind of their creators you'd have to ask each one how their zombie set achieves locomotion.

One theory is that the virus changes walkers so that they get energy from photosynthesis. This is supported by the fact that walkers are less active than unchanged humans, just like plants are. Plants also use photosynthesis to get energy and they're not very fast moving either."