I am going on a ski trip in France, at Courchevel 1650. We are taking the TGV to the "Moutiers Salins Brides Les Bains" station.
How will I get from the train station to my hotel (which is right at the base of the Courchevel 1650 piste/slope?
There are no train lines to all stations. As pnuts comments, Belle Savoie Express has a bus line from Moutiers (train & bus station) to Courchevel 1650.
Here you can find the timetable (pdf file): http://www.mairie-courchevel.com/download/PRATIQUE/Transport/2014-2015/lr_t5_la_tania_-_courchevel.pdf
Can also be found here (more dynamic where you can select travel date, and a map of the stops!): http://itineraire.mobisavoie.fr/en/line-timetables/6/LineTimeTable/courchevel-moutiers/369/courchevelgareroutiere-saintbontarentaise/1?KeywordsLine=Courchevel%20-%20Mo%C3%BBtiers&OperatorId=9
The stop may be
COURCHEVEL-MORIOND-OFFICE-DU-TOURISME for you in this website.
You can get your tickets here: http://www.mobisavoie.com/7492-achat-d-un-billet-de-car.htm
COURCHEVEL Moriond 1650
You can then select if your want tickets sent by mail, or etickets that cannot be modified or canceled.
For your information, here is the map of Courchevel 1550 - 1650: Courchevel map
There are also a number of taxi companies that will take you from the train station at Moutiers to the various Courchevel resorts: http://www.courchevel.com/winter/en/taxis-rs93.html
Prices start around 65€ one way for 1-4 people.