Buses leave from Dehradun train station. There are two buses which go to opposite ends of the Mussoorie Mall, Library and Picture Palace. It is quite a hike from one to the other, so make sure you catch the right one. To reach Kempty Falls directly from Dehra Dun catch a bus from the Dehra Dun Railway station Hill Bus Services Section or take a taxi. One should look for buses heading for destinations like Barkot, Nainbagh, Yamunotri, and Purola (Caution:sometimes Purola buses go via Vikas nagar which may take you off the route completely so be careful). You can also take a bus to the Library end of Mussoorie and walk to the Kempty Bus stop and take a bus or taxi or a milkvan or even hitch a ride with a tourist going in that direction!! Toll Tax is payable on entering Kempty Village per bus/taxi/car/scooter.
It is possible to hire a taxi for the trip up to Mussoorie. Rates should be around Rupees 400-550 but one can pay per seat as well in a shared taxi which normally accommodates upto five passengers.Shared or chartered taxis too are available near the same Hill Section Bus terminal and the rates are controlled by the taxi union. These rates are generally displayed on a board outside their office.
For the most part you will want to get around on foot. The Mall is closed to most vehicles.
A relatively flat section of the Mall allows a fleet of rickshawalas to ply their trade. You can catch a ride from the Library end of the Mall to about the midpoint.
Within Mussoorie, taxis are not very useful. If you are heading up to Landour with your luggage, it would be wise to catch a ride. They can also be hired for outings to places such as Kempty Falls or Happy Valley. There are taxi stands at both ends of the Mall. Many locals offer 'taxi' services, and if you are staying longer you will likely find these (slightly cheaper) alternatives.