You need to follow Ambala-Zirakpur Expressway on National Highway(NH) 44 and Zirakpur to Shimla (111 km) on NH5 in Himachal Pradesh. Shimla to Narkanda-Rampur Bushahr-Powari-Pooh-Dubling village drive is on NH5. Dubling village to Nako-Tabo-Kaza drive is on NH505. Kaza is the headquarter of Spiti valley.
How to reach Spiti valley from Delhi?