How do I make prefab follow a gameobject?(C#)

Hi. I have been trying to get a prefab instantiate and then follow a gameobject in C#. The prefab is instantiated in the script that is attached to the gameobject, but the prefab doesn't change its position once it has been instantiated.

     void Start ()
     {
         Vector3 firePosition = new Vector3(transform.position.x, transform.position.y, transform.position.z);
         Instantiate(FirePrefab, firePosition, Quaternion.identity);
     }

I have tried to put the firePosition in the update function, but I am not sure how to get that to work (Is that even the right way to do it?)

Does anyone know how I can do this? Thanks in advance :)