Its always fun to answers anything which has a reference with this TV series Pretty easilly, eventually. If this event ever did start the best thing you could do is get the hell out of any large metro area, Chicago foe instance would be one of the worst places to be given the number of walkers vs living people with weapons would be so bad.
If you did find yourself somewhere and couldn't get out the best thing to do is find yourself a grocery warehouse, clear it, fortify it, get access to the roof and prepare to collect rainwter and do small scale gardening in pots. Use up any perishables as fast as possible or remove them from the building before they spoil. If there is only a small group of people one grocery warehouses non perishables could support you for a few years if you had the right setup to go along with it.
Also you may be able to use gasoline vehicles for maybe a year or two. After that most gasoline will be useless. You'll want to find yourself a diesel, even old diesel fuel can be used if filtered first to remove sediment and fungus. Also you can use vegetable and canola oil blended with diesel or possibly on their own. Many aspects of TWD (aside from the zombies) are unrealistic.
For instance having to go poke walkers off the fence at the prison. Why not just get a tractor with a front end loader bucket and make a lap around the prison a few times a day? But that wouldn't make for a good TV show. And even after seeing the Governor's “walker traps' the prison group failed to use this useful tactic after seeing how they worjed. They should have had walker traps all around the prison.
And why wait on the walkers to come to the fence? Go out and run a patrol any time you're able. Walkers are easy to kill when they're in small groups (say 1–5) even for a single person. But when you get too many in one spot they can advance faster than you can shoot.
As for the military? It'd be a pretty quick learning curve. If it looks bad, two to the head, next customer.
I think you'd probably lose a lot of people in major metro area, out in the rural US? Most folks who live out here can handle their own when it comes to guns. I think you'd have a lot of good old boys riding around in pickups cleaning up the trash.