The closest major airport is Geneva. You could easily rent a car at the airport and drive, but you will not need a car while you are in the resort, and you will have to pay to park it.
Bus service runs almost every hour from the Geneva airport. Pass out of the baggage claim area to the counters by the door. The bus desk, called the Gare Routiere, is to the right of the door next to Hertz. Buy your ticket, actually two tickets. The first stop is Moutiers where you change buses for Courcheval. To get to the bus, pass out the door to the left of the ticket counter and walk straight out past the pick up area to the line of busses. Look for one with Moutiers in the front window. By the way, you need to pay for the ticket in Swiss francs ( they do not use the Euro in Switzerland!). I'd suggest charging it on a Visa.
If you prefer to take the train, the TGV train runs from Paris to Moutiers, where the train station and bus station are adjacent to one another. I think the train leaves Paris from Gare de Lyon. Moutiers is a very short distance from Meribel and Courcheval.