There are many daily flights between Delhi and Dehradun, with airlines such as Jet Airways, Spice, Air India and Indigo offering multiple flights and times. You could check out the respective airlines online booking or websites such as http://www.cleartrip.com to book.
There are many trains available daily between Dehradun and New Delhi (Railway station – Ph: 0135 – 262-2131/262-4002). Other major cities connected by rail are Lucknow , Varanasi , Mumbai and Calcutta . From the station you can take a bus, an auto rickshaw or taxi to your destination in the city. http://etrain.info/in will provide you with the train schedules when you type in the city names.
You can take a taxi or bus to Dehradun from any of the neighbouring state or town. The drive from Delhi takes approximately six hours. Buses arrive in Delhi at the Bus Stand on Gandhi Road, and in Dehradun the buses arrive at the Mussoorie Bus Stand near the railway station or the City Bus Stand near the Parade Grounds. There are regular services connecting Mussoorie, Haridwar, Nainital, Kullu, Shimla, Agra and Delhi.