There is a very simple damage system included that can be easily extended to work with your own custom setup.
A "Damageable" component has a health value. Damage can be dealt to it by calling it's DealDamage(float damageAmount) method. Once this value is <= 0 then the "DestroyThis" method will be called.
The "DamageCollider" component can be added to colliders. Whenever this collider collides with an object that has a Damageable component, the specified amount of damage will be dealt.
If you want to integrate with another damage system, just override the "DealDamage" method and pass along the damage value. Here is an example of how to integrate with EmeraldAI's damage system: