As anyone who has played one of the "Silent Hill" games knows, surviving zombies is no mean feat. Even if the Zombies didn't try to kill you, the subsequent collapse of human infrastructure can make maintaining a daily routine difficult. In addition, of course, there exist hordes of mindless, soulless psychopaths that want to kill you. The first thing to do is find a weapon. In lieu of finding firepower, I recommend the lead pipe, or similar implement. This item, while heavy, commands respect when used appropriately. This means that one weilds the lead pipe like they would a cue stick in pool. Imagine the cue ball to be located in front of the zombie's face or solar plexus. Grip the rear end of the pipe while letting the pipe slide through the front hand. This will allow you to strike hard and fast while minimizing the expenditure of energy necessary for each blow.
I would also recommend reserving overhead chopping motions, such as you would use with an axe, only for "kill strokes" when the zombie(s) are already immoblized. In case you have never chopped wood, bring the pipe over your head and, as you bring it down, let the forward hand slide down the shaft. This will lend power and accuracy to your stroke. Attempt to crush the cranium. This type of attack can be very tiresome, as anyone who has made fire wood knows, and running might be necessary at a moments notice.
Also of zombie fame is the chain-saw. While powerful, this has some unfortunate handicaps. For one, the range of the chainsaw is very limited. You have to get too close to a given zombie. The chainsaw is not only heavy but unweildly, making the removal of multiple zombies a slow and dangerous process. Three: It needs a gas/oil mixture. Even if you can find gas, no one wants to be siphoning some gas out of a nearby SUV and trying to get a 10:1 ratio of oil into their chainsaw while the zombie horde approaches. Four: Bodily fliuds, and lots of them. This could be an infectious disease, folks. Don't get splatted.
While you are doing this, take care to avoid contact with the bodily fluids of zombies, as these may be vectors of infection. Other common implements -- such as knives, baseball bats, and mop handles -- are limited either in range (knife) or in the amount of damage that they can deal (bats and brooms). Of course, there is always the unclaimed treasure trove of high-power ordinance or melee weapon extravaganza, but these could prove rare.
But with a little luck and a little ingenuity, we should all be safe regardless of how many of them there are.