In reply to joe.91:
Funnily enough, I've just been looking into this as a couple of friends want to join us in Cogne this winter via public transport from either Geneva or Turin - and they can't be @rsed to do the research for themselves!
1/ There's the (already mentioned) Geneva-Chamonix shuttle. Then there's a regular bus service between Chamonix and Aosta.
http://www.chamonix.com/pdf/courmayeurete.pdf
2/ There's a direct bus from Turin Caselle Aiport to Aosta that runs a couple of times a day, timetable as follows:
DEPARTURES TO AOSTA
Departure Location: Arrivals level
Frequency: Twice a day
09:30 Monday to Friday
10:45 Saturday and Sunday
22:15 Daily
3/ Otherwise you can get the airport bus to Turin's Porta Nuova train station and get the train to Aosta :
http://www.trenitalia.com/cms/v/index.jsp?vgnextoid=ad1ce14114bc9110VgnVCM1... has timetables in English.
4/ Buses run regularly between Aosta and Cogne, although less frequently at weekends.
As we'll have a car out there already, my friends are determined to do it without hiring a car, but as David says I also reckon that hiring a compact car will hardly be any more expensive (if at all) and be far far less hassle, all things considered. Turin to Cogne by car is straightforward and only takes 2-3 hours; Geneva to Cogne obviously less so and then there's the 40 euro MB tunnel toll charge to consider too.
HTH
Dave