It is very convenient to reach Tirthan.
You will have to take a bus of Manali from Delhi. Get down at Aut(50 kms before Manali). Take a taxi from Aut till Tirthan Valley. So it is:
Delhi- Aut-Tirthan
Take himanchal state roadways bus till Aut. From there, take a taxi to Gushaini. There are lots of homestay to opt. I will suggest, you try and book with Raju's cottage. His location and food is awesome.