Hey Ayush,
Take a direct state transport bus to Joshimath. From Joshimath, you can take sharing vehicles to Auli ( 15KM). Options for accommodation are limited and costly in Auli so stay in Joshimath.
The best option is to a book a cab from Dehradun to Auli.
Happy travelling!!!!!!
It's a 350km journey and you can either take a bus from rishikesh or best, you should hire a cab till Joshimath from which you'll have to go to auli by cable car because roads gets blocked at this time of year.
Happy Travelling
If you are going not by your own vehicle than their are state transport buses that will help you till Joshimath further like most travelers you can take shared accommodation till Auli.
Happy travelling!!
Dehradun to Haridwar Via Train
Haridwar- Auli- Haridwar Via Cab
Dehradun till Haridwar. Catch train that runs in the evening / late night from Dehradun and reaches Haridwar early morning so after a brief halt, you can proceed for Auli.
Day 1 Start the early morning by 05- 06 AM Haridwar to Joshimath. Take Cable ride from Joshimath to Auli (25-35 min ). Overnight at Auli.
Day2. Auli sightseeing and activities.
Day3. Auli sightseeing and activities.
Day4. Auli to Joshimath via Cable Car ( starts morning at 09:00 AM ) and Joshimath till Haridwar/ Auli. Catch the train from Haridwar late evening to reach Delhi early morning.
Good Luck!!!