How to make object move where the camera points?

I've been trying to setup a first person movement script, and the problem I've found is it will only move on the X axis, and Z axis, as a global position. I'm wondering how would I go about making it so, that when I point it in a direction it will swap it's axis to that direction, if that makes sense. Basically, how would I go about making a first person movement script work.

 using UnityEngine;
 using System.Collections;
 
 public class FPSMovement : MonoBehaviour
 {
     public Camera FPSCam;
     public float speed = 4.0f;
     public float runSpeed = 4.5f;
     public float Stamina = 100.0f;
     public float gravity = 20.0f;
 
     private Vector3 moveDirection = Vector3.zero;
     private CharacterController controller;
 
     // Use this for initialization
     void Start()
     {
         controller = GetComponent<CharacterController>();
     }
 
     void run()
     {
         if (Stamina > 0.0f)
         {
             moveDirection *= runSpeed;
             Stamina -= Time.deltaTime * 2.0f;
             Debug.Log(runSpeed);
         }
     }
 
     // Update is called once per frame
     void Update()
     {
         if (controller.isGrounded)
         {
             moveDirection = new Vector3(Input.GetAxis("Horizontal"), 0, Input.GetAxis("Vertical"));
             moveDirection = transform.InverseTransformDirection(moveDirection);
             moveDirection *= speed;
 
             if (Input.GetKey(KeyCode.LeftShift))
                 run();
             else if (Stamina != 100)
                 Stamina += Time.deltaTime * 2.0f;
         }
         moveDirection.y -= gravity * Time.deltaTime;
         controller.Move(moveDirection * Time.deltaTime);
     }
 }