Chalet Stephen is readily accessible by road, rail and air.
The trip is about 90 minutes by road. Here are some maps and directions to help you (in Adoba Acrobat form)
Map of route
Directions
Turn by turn instructions
It is quite feasible to get a taxi from the airport if you want to arrive in some style and comfort. The cost is likely to be in the region of 100euros. You should book in advance rather than take a cab from the stand, though. There are several companies including Vachoux
There is a fairly good link between Geneva and Evian. You will ned to get a taxi or other local transport from Evian (about 12km).
Geneva airport has its own railway station but you will have to change in the city for the line to Evian. The trip takes between 2 hours and 3 and a half hours. Timetables and reservations are available on the SNCF site.