have basic controllers, need flying

hey, peeps, need help,

have a bird, rigid body with gravity enabled, character controller and this script, how can I make it fly? something like pressing space and it gets up in the air and stuff... just started working with unity, eem, scripting skills close to 0, that's why probably struggling)

thanks in advance!)

 using UnityEngine;
 using System.Collections;
 
 public class PlayerScript : MonoBehaviour {
 
     private Animator anim;
     private CharacterController controller;
 
     public float speed = 6.0f;
     public float turnSpeed = 60.0f;
     private Vector3 moveDirection = Vector3.zero;
     public float gravity = 20.0f;
 
     void Start () {
         controller = GetComponent <CharacterController>();
         anim = gameObject.GetComponentInChildren<Animator>();
     }
 
     void Update(){
         if (Input.GetKey ("up")) {
             anim.SetInteger ("AnimParameter", 1);
         }  else {
             anim.SetInteger ("AnimParameter", 0);
         }
 
         if (Input.GetKey ("down")) {
             anim.SetInteger ("AnimParameter", 1);
         }  else {
             anim.SetInteger ("AnimParameter", 0);
         }
 
         if(controller.isGrounded){
             moveDirection = transform.forward * Input.GetAxis("Vertical") * speed;
         }
 
         float turn = Input.GetAxis("Horizontal");
         transform.Rotate(0, turn * turnSpeed * Time.deltaTime, 0);
         controller.Move(moveDirection * Time.deltaTime);
         moveDirection.y -= gravity * Time.deltaTime;
     }
 }