Are you heading from delhi?
You can take local transport also..plenty of buses for dehradun and then to mussorie..it’s very beautiful..kempty falls are amazing..visit mall road and enjoy the local pastry from local bakers and lot more
To explore Mussoorie the best way is to rent a bike or a vehicle, you can start from D'dun where you can get rental vehicles very much easily. Public transport is not reliable in Mussoorie and you can't cover all the places by using it. Mussorie lake id over hyped and nothing to see there great so you can skip it, choice is urz.
Visit Kempty falls, bhatta falls, gun hill point, George Everest point, camel back road.
Stay at mall road, enjoy shopping and local meal over there. From there you can visit Landour and Dhanaulti. Plan accordingly.
Firstly you have to reach ISBT dehradun. From there you'll get plenty of busses and other local cabs to reach mussoorie. After reaching Mussoorie you'll find may tour guides appoint one of them and they'll guide you further
I have attached with this comment a perfect package for you to explore Mussorie and nearby places, you can click on them to find more details about them. If you want to talk to someone about the packages simply fill in your details in the form and you will receive a call.
Reach Delhi first..... From Delhi ISBT, you will have many buses plying to Dehradun... You also have got many trains between Delhi and Dehradun.... From Dehradun, you will have many state buses going to Mussorie...