While attemtping to save the girl at the church you'll find yourself captured by unfriendly humans and forced to fight zombies for their entertainment.
You'll start in a cage, but once it's lifted off of you you'll have a few moments to grab supplies before the first wave of zombies is released. Ahead you'll see a bird bath with a handgun and ammo. There will be a couple of wrecked cars in the arena with ammo on/in them as well.
Once the first wave of zombies is released get them to follow you passed one of the propane canisters and shoot it when they are near. Repeat as necessary for other groups of zombies. A couple of exploding zombies will show up as well and you should try to hit them when other zombies are near.
Eventually a second area will open up. There will be a ramp you head up passed a bus. On the ramp grab the mine and use it when needed. A second mine can be found on a catwalk at the rear of this new area. Again, use as needed.
Once you've killed enough zombies you'll be able to hit a button and open a door that will lead to your gear. At this point a ton more zombies will show up so keep moving and make your escape.
Basically, keep moving, conserve ammo, and try to kill zombies in groups with explosives.