As you progress through checkpoints during the Road Raid you can use the rocket button on the bottom right corner of the screen. 

It allows you to boost through Zombies withouth requiring the vehicle to stop and your preppers fight. 

Once you hit a checkpoint without boost your preppers will bet out of the vehicle to fight Zombies or Zombie Bosses. 

To beat tougher opponents you can use one of the 3 charged abilities you have. 
Each prepper has 1 ability they bring to the fight (green icon will indicate the ability is charged and ready to use while grey means it's still on cooldown). 

The type of weapon your prepper is carrying can effect the ability they have. 
Once you have cleared a couple of checkpoins or a Boss click on the loot button and collect rewards.