How to send out troops for killing zombies?

Go to the world view and find a zombie to tap on. Normal zombies are on a single tile while the boss zombies (Wendell the Clown, plus others from time to time) take up 4 tiles.

Normal zombies you can attack yourself. Tap on one and then tap the attack button. Choose your APC to send to them. You must start with low level ones, and increase in level 1 at a time. (you cannot attack a level 5 before you have killed a level 4 for example).

Attack these at any time, the game will tell you if they are too strong for you to attack. Add more troops and level up APC research and heroes to make your march stronger.

The boss zombies must be rallied (a team attack with other alliance members). See How to rally against Wendell the Clown for more details .