You have to get down at Rudrapryag for which you can take a direct bus from Delhi!
if in case you don't find a direct bus you can take the one that goes to Srinagar, Karnpryag or Guptkashi. Make sure you book them online prior to your visit because only one bus runs each day! After getting down at Rudrapryag, take any Bus or shared sumo to Ukhimath, From Ukhimath take a taxi for Chopta. And about the stays, there're camps, tents, lodges & hotels available in Chopta. :) You might wanna stay in chopta only because they're hardly any accommodation available in Tungnath.
Delhi-Dehradoon-Rudrapryag by train and bus
Rudrapryag-Ukhimath-Chopta by shared taxi or jeep.
Chopta and trek to Tungnath. **Limited options to stay at Tungnath, check and book in advance. Share your blog once u do this trip