Notes on everything: How to make the camera follow a GameObject

How to make the camera follow a GameObject

At first, save this as "SmoothFollow.cs" in the Assets folder.

using UnityEngine;
using System.Collections;

public class SmoothFollow : MonoBehaviour {

    // The target we are following
    public Transform target;
    // The distance in the x-z plane to the target
        //So this would be your offset
    public float distance = 10.0f;
    // the height we want the camera to be above the target
    public float height = 5.0f;
    // How much we 
    public float heightDamping = 2.0f;
    public float rotationDamping = 3.0f;

    // Place the script in the Camera-Control group in the component menu
    [AddComponentMenu("Camera-Control/Smooth Follow")]

    void LateUpdate () {
        // Early out if we don't have a target
        if (!target) return;

        // Calculate the current rotation angles
        float wantedRotationAngle = target.eulerAngles.y;
        float wantedHeight = target.position.y + height;

        float currentRotationAngle = transform.eulerAngles.y;
        float currentHeight = transform.position.y;

        // Damp the rotation around the y-axis
        currentRotationAngle = Mathf.LerpAngle(currentRotationAngle, wantedRotationAngle, rotationDamping * Time.deltaTime);

        // Damp the height
        currentHeight = Mathf.Lerp(currentHeight, wantedHeight, heightDamping * Time.deltaTime);

        // Convert the angle into a rotation
        var currentRotation = Quaternion.Euler(0, currentRotationAngle, 0);

        // Set the position of the camera on the x-z plane to:
        // distance meters behind the target
        transform.position = target.position;
        transform.position -= currentRotation * Vector3.forward * distance;

        // Set the height of the camera
        transform.position = new Vector3(transform.position.x,currentHeight,transform.position.z);

        // Always look at the target
        transform.LookAt(target);
    }
}