Detailed sequence:
1- Drag the Fireworks effect to the scene and position it where you want; uncheck its field Emit in the Inspector, or the fire work will keep exploding forever;
2- Attach the script below to the trigger object;
3- Select the trigger object, then in the Inspector click the field Fire Work in the component Trigger Goal: this allows selection of the Fireworks effect you've placed in scene;
Presto! It's ready to play!

public class TriggerGoal : MonoBehaviour;{

  public ParticleEmitter fireWork; // this will appear as Fire Work in the Inspector 

  void OnTriggerEnter(Collider other){ 
    fireWork.Emit();
  }
}

NOTE: The Fireworks effect will explode whenever any rigidbody or CharacterController enters the trigger. If you want to fire the effect only when certain objects enter the trigger, you may compare other.tag to some specific tag:

  void OnTriggerEnter(Collider other){ 
    if (other.tag == "SomeTag"){ // only SomeTag tagged objects will work
      fireWork.Emit();
    }
  }

Remeber to tag the objects accordingly, if you want to use this alternative.

To emit particle, you will need a reference of the particle system component. The easiest to do that is to declare the variable as public and of type ParticleSystem (ParticleEmitter if it's not the new particle system). It's going to look like that :

// the first letter of fireWork being a lower case is just a convention.
public ParticleSystem fireWork; 

Then, you need to detect th collision. When the physic engine detect a collision, it sends a message to the game object being collided. If its collider is a trigger, that message is OnTriggerEnter. By implementing that function, you can receive the message. Now you need to make the emitter emit. For the new system, it would be fireWork.Play(); For the old one, fireWork.emit = true or fireWork.Emit();