Make my gun model fire bullets

There is no Physics.Raycast() call here, so this code takes an uninitialized RaycastHit structure and accesses the uninitialized 'hit.point'. I believe 'hit.point' in this situation will be Vector3.zero, so you code just moves the projectile to Vector3.zero in world space.

Alright, bit of an update. I made some edits to my code after looking up Physics.Raycast() at your mention. I discovered that I needed arguments, so I kinda just winged it. I'm shooting in the dark, in case you couldn't tell :) New code:

 using UnityEngine;
 using System.Collections;
 
 public class PlayerGunController : MonoBehaviour 
 {
     public GameObject projectile;
     public int speed = 10;
     public int ammo;
     public RaycastHit hit;
 
 
 
     void Update() 
     {
         Vector3 fwd =  transform.TransformDirection(Vector3.forward);
         if(Input.GetMouseButtonDown(0)) 
         {
             if(Physics.Raycast(transform.position, fwd, Mathf.Infinity))
             {
                 projectile.transform.position = hit.point;
             }
         }
     }
 }

Nothing appears to have changed. I click the mouse button, and the capsule disappears. Having the scene view and game view windows side by side with the capsule object highlighted, I noticed that when I click, the capsule drops below the terrain and follows the character around from there. I have the capsule parented to the gun, which is parented to the main camera from the stock FPS Controller.

Before changing the transform.position of the bullet, you have to set it's parent to null.

projectile.transform.parent = null;

As for the movement, you are still not lerping the bullet but rather make it go to the hit.point position instantly from one frame to the next.

BTW, you can just use transform.forward as the raycast vector3.

Thanks for that^^ But I'm a little confused... The few times I've seen Lerping in use(in tutorials and such) it was only a couple of lines of code. THis is what's in the link you gave me

 using UnityEngine;
 using System.Collections;
 
 public class ExampleClass : MonoBehaviour {
     public Transform startMarker;
     public Transform endMarker;
     public float speed = 1.0F;
     private float startTime;
     private float journeyLength;
     public Transform target;
     public float smooth = 5.0F;
     void Start() {
         startTime = Time.time;
         journeyLength = Vector3.Distance(startMarker.position, endMarker.position);
     }
     void Update() {
         float distCovered = (Time.time - startTime) * speed;
         float fracJourney = distCovered / journeyLength;
         transform.position = Vector3.Lerp(startMarker.position, endMarker.position, fracJourney);
     }
 }

By my understanding, I'd need to declare the start point(the player's position)and the end point(The raycast hit point?), plus another bit to actually perform the process. The example code in the documentation seems really intensive for doing something as simple as that. What I'm asking is, do I really need all 20 odd lines in the example?

No, it can just be a simple while... loop in a simple Coroutine with only abour four variables.

There are a lot of tutorials on this so you will just have to read a bit :) After all, it is one of the most basic and often-used functions in Unity.

    private bool moving;
 public float speed = 2.0f;
 public Vector3 targetPos;

 void Update() {

     if(moving == false) {
         moving = true;
         StartCoroutine(Move(targetPos);
     }
 }

 IEnumerator Move(Vector3 newPos)
 {

     for (float t = 0.0f; t < 1.0f; t += Time.deltaTime * speed) {
         transform.position = Vector3.Lerp(transform.position, targetPos, t);
         yield return null;
     }
             moving = false;
 }

Where targetPos would be hit.point. You use the portion

         if(moving == false) {
         moving = true;
         StartCoroutine(Move(targetPos);
     }

whenever you want to set the bullet in motion (so, after pressing the fire button for example).