How to make player move according to camera's rotation

I have a script that currently makes the player run the direction the camera is facing. I want to make it so that whenever I press a or d that the player will run to the left or right of the direction that the camera is facing. Also, I want to make it so when I press the s key that it will run back towards the camera. If you have ever played Assassin's Creed, that is the kind of movement I'm looking for. Here is the script I currently have:

 if(Input.GetKey(KeyCode.W) && Input.GetMouseButton(1)){
                 if(anim.GetCurrentAnimatorStateInfo(0).IsName("Running")){
                     GetComponent<Rigidbody> ().velocity = Camera.main.transform.forward * Input.GetAxis ("Vertical") * 6f;
                     Vector3 rot = transform.eulerAngles;
                     rot.z = 0f;
                     rot.y = Camera.main.transform.eulerAngles.y;
                     transform.eulerAngles = rot;
                 }
             }