How do you maintain gravity using transform.forward and transform.right?

I'm making my own first-person game and I have this problem where whenever I move after jumping, the player slowly falls to the ground. I know that when I use transform.forward the y values of the player are being set to 0 and the downward force is basically being reset, that's why it falls slowly. I just need help finding a way to maintain the gravity of the player.

I know I can use a character controller and all that, but I want to learn how to do it this way. I'm willing to change the code around, I just don't want to use a controller. Thanks :)

Here's the code:

     void Update () {
         if(Input.GetKey(KeyCode.A)){
             transform.position += -transform.right * Speed * Time.deltaTime;
         }else if (Input.GetKey(KeyCode.D)){
             transform.position += transform.right * Speed * Time.deltaTime;
         }
         if(Input.GetKey(KeyCode.W)){
             transform.position += transform.forward * Speed * Time.deltaTime;
         }else if (Input.GetKey(KeyCode.S)){
             transform.position += -transform.forward * Speed * Time.deltaTime;
         }
     }