update: i forgot to post this, it might be useful. i've been experimenting with this method (for mouse first) that i learned on answers earlier

function Update () {
    var ray = Camera.main.ScreenPointToRay (Input.mousePosition);
    var hit : RaycastHit;
    if (Physics.Raycast (ray, hit, 1000) && hit.collider.gameObject.CompareTag("GameController")) {
        self.position = hit.position;
  }
}

For touchscreen stuff, you'll be wanting to use Touch events. Essentially, you can replace all your references to mousePosition with the appropriate touch events.

It contains the same mouseDown/mouseUp kind of events as you're used to, but they're contained in TouchPhase.

I'd advice checking out the DragRigidbody script that's included in Unity (if you don't have it in your assets folder, import it). It works perfectly and could serve as a good example for you.