Transport from Grenoble to Vaunières

As you can see on the map if you zoom in a little, the nearest train station is Lus-la-Croix-Haute. The trip from Grenoble takes about an hour and a half, it should appear as a result on the SNCF website, or you can see the timetable here. To reach Vaunières, maybe you could use a taxi or a car rental, I am not able to find any public transport option.

In France, public transportation is managed at multiple administrative levels. SNCF runs most of the trains, with shorter-distance trains operated on behalf of the regional councils. Buses are a mixture of private companies and public authorities, coordinated at the level of régions, départements or communauté de communes/d'agglomération/urbaine (municipalities and groups thereof). I'm not aware of any single information source for the whole country, you need to search for information on the appropriate local website (often in French only). Usually, for places that aren't on a major train line, the best place to start looking is on the website of the municipality; search for “transports” or “accès” or “comment venir” (how to come). Gare is a train station, gare routière is a bus station, car is an intercity bus, arrêt is a bus stop.

The Hameau de Vaunières is on the municipality of Saint-Julien-en-Beauchêne, whose website doesn't mention transportation except to state that the nearest train station (gare) is Lus-la-Croix-Haute (6km away — and note that Vaunières is further up the mountain from the village). If you're going to the Village des Jeunes, contact them to see if they might send someone to pick you up; this is pretty common with rural accommodation.

If you want to make your own way, the website of Lus-la-Croix-Haute has an “Access” page which gives several pieces of information:

• The train station is on the line between Grenoble and Gap. You can find more information on the regional trains website, including the train schedule (approximately one train every 2 hours).
• There is one daily bus between Grenoble and Marseille (line 31 of the Rhône-Alpes bus network).
• There is no regular local bus service, but there is an on-demand service called Transdrôme (operated by the département), reserved for people arriving by public transport and whose final destination is in a town not served by public transport (or the other way round). This service needs to be booked by phone or email at least 24 hours in advance. It doesn't operate on Sundays. If you want to use that, contact them early — some locales ask for a booking 48 hours in advance and their web pages don't seem to be very up-to-date. If the service operates, ask for confirmation that Lus-la-Croix-Haute is the place where you'd need to transfer and not some larger town.
• The phone number for the local taxi (see the website).