Move left etc. according to where player faces

How can I make it so that the player goes right when he presses "D"? I've been trying things like this

 rigidbody.velocity = -(Vector3.right * speed * Time.deltaTime);

But it moves according to the XYZ space, not depending on where the player faces. The movement I'm trying to get is like in FPS games. I do not want to use Character Controller.