Example.cs

// Public domain - Alexander Taylor

using UnityEngine;
using System.Collections;

public class Example : MonoBehaviour {
	public Transform player;
	public float speed;

	bool isDragging = false;
	Vector2 offset;

	void Update() {
		// Intially touched the screen
		if (Input.GetMouseButtonDown(0)) {
			offset = Camera.main.ScreenToWorldPoint(Input.mousePosition) - player.position;
			isDragging = true;

			// Released the touch screen
		} else if (Input.GetMouseButtonUp(0)) {
			offset = Vector2.zero;
			isDragging = false;
		}

		if (isDragging) {
			Vector2 destination = (Vector2)Camera.main.ScreenToWorldPoint(Input.mousePosition) - offset;
			player.position = Vector2.MoveTowards(player.position, destination, speed * Time.deltaTime);
		}
	}
}