How to keep the player on the left side o the screen?

as @highpockets write, you can attach camera as a child of the player, however if you need a animated, less rigid or "natural" following, I did a script about a month ago, is similar to a ton of scripts that are already on the net, so I dont think to is a great discovery:

 public class SlowFollower : MonoBehaviour {
     public Transform Target; //target to follow
     public Vector3 PositionFollowing;//position of the camera relative to the target 
     Vector3 PosBuffer = Vector3.zero;
     Quaternion RotBuffer = Quaternion.identity;
 
     // if u are using physics to move the player, to evade camera jittering use LateUpdate but, if it dont work like with me, use FixedUpdate 
     void FixedUpdate () {
         if (Target) {
             //chek if target change position or rotation
             if (!((PosBuffer- Target.position).sqrMagnitude < .001f)
                 && Quaternion.Angle(RotBuffer, Target.rotation) < .05f) {
 
                 SlowFollowing();
                 PosBuffer = Target.position;
                 RotBuffer = transform.rotation;
             }
         }
     }
 
     void SlowFollowing(){
         PosBuffer = Target.position + (transform.forward * PositionFollowing.y + 
             transform.right * PositionFollowing.x - 
             transform.up * PositionFollowing.z);
         //u can change this to make a fast or slow following, to change position use lerp, this tweak just work if divide with 2
         transform.position = (PosBuffer+transform.position)/2;
         transform.rotation = Quaternion.Lerp (transform.rotation, Target.rotation, .2f);
     }
 }

Cinemachine is what you need.