Guns start to become more available in Act 2. You will start to run into humans (killing them for the humanitarian achievement), and most of them will be carrying guns. When you finally acquire a gun, continue to collect ammo until you max out.
Also be on the lookout for guns that drop from humans and if the stats are better then your current gun, replace it. When you have a good gun and max ammo for it the hard part is now over.
All that is left is to find a group of zombies and lure them to a car, which if you are still in the city in Act 2, you wont have to look very far. Jump on top of the car and the zombies will group around, but will not be able to climb on top. They may move around a bit at first, but it is only to try to get closer to you so find a good spot and wait for the zombies to stay still and raise their arms toward you.
Once you have your spot and the zombies are in place. Aim down with Left Trigger and nab some easy head shots. Do not worry if it doesn't kill them instantly, sometimes even a direct head shot wont kill them with one bullet (which is why you picked up all that ammo :) ). After the group has been killed jump off and repeat with a new group.
If needed you can upgrade your gun however many times you wish but I was able to get it done with what I had. Good luck and have fun slaying some zombies!