Air: Jolly Grant Airport (DED) is a newly constructed airport in Dehradun and connects major cities with daily flights. The airport has indeed been a major plus point for tourists.
Rail: Dehradun Terminal (DDN) is presently the nearest station and from here on you need to board a taxi. It takes close to an hour from here to reach Mussoorie.
Road: Buses from Delhi are plenty. If planning to go on a 8-hour self-drive, the route you should follow is Delhi – Meerat – Muzzaffarnagar – Haridwar – Dehradun – Mussoorie. If starting from Chandigarh, then take the National Highway 7 all the way to Mussoorie and takes around 5 hours.