Well, there's a few different ways it could progress. 

First way, patient zero gets bitten or infected from something somewhere. Patient Zero wanders home, dies, turns, bites, someone else, maybe several someones before he is restrained or killed. They die and turn, and bite several someones, and so on. Typical Class 1 outbreak scenario as detailed in Max Brooks' works. The problem with this, is that with quick thinking and coordination such an event could be stopped in it's tracks. 

Second way is that there's something in the water, food supply, or air that gets spread through the population. It may have hopped species from the animal kingdom, but is now among people. People start to become sick with flu-like symptoms, high fever, bad chills, severe body aches, tiredness, delirium, dehydration, nausea. After a few days to a week they begin to expire, in waves and droves. And then after a while, 10 hours or more they start to reanimate and resurrect, and that's when the real horror begins.

I could think of one or two more ways this could work, but it wouldn't be close enough to the Walking Dead to call it that anymore.