You have to lure all zombies to town in order to get rid of them all at once.
Use the cemtary on the lower right, next to the big house (don’t walk over there, use it). Use the second left stone from the top row to break a piece of STONE off. When you mess with the zombie, it’ll folow you all around but it’s a good zombie so don’t worry.
Leave the graveyard on the left and go to the shop on the upper left. Inside you can take the FOOD, CRAP CUP and the HAND OF DEATH. Talk to the shopkeeper and learn about the zombies in town and the one on the graveyard. Leave the shop at the lower left corner.
Go to the middle top building: the bar. Talk to the zombie at the top to see what’s bothering him. It’s the zombie at the bottom. Use the zombie at the top to get the KEY. Talk to the other zombie and he’ll say otherwise. Use this zombie to get the MATCHES. Use the matches on the lower zombie to kill him. Leave the bar also in the lower left corner.
You might want to check the Zombie Mayor’s house and talk to the zombie there. Nothing new though. Leave the house on the lower right. Follow the path to the right and meet the zombie god. Give the food, matches or crap cup to end it all.
Game source: A copy of the game was found here on the internet.