You'll have heard a discount Chamonix bus operator starts up for the 2014-15 season. For sure, Geneva to Chamonix for 5.99 euros is pretty darned amazing, but it's terrific only if a drop off at Chamonix train station suits.
Now, you do know, that the Chamonix ski resort is not a centralized resort. You'll need to figure out the orientation of the valley as the ski regions and accommodation are spread across the valley. Cham is not a central type of resort with ski lifts radiating away from the base and it does take about an hour to get from one end to the other.
This could mean a door-to-door service may well be more convenient. There's more than enough local services to ensure reliable service at competitive prices. You could look up:
These services also have private car transfers if so desired.
The new very inexpensive service is provided by Easy Bus from Geneva airport to (only) the Chamonix Mont Blanc railway station. You'll have to make your own way from the station, if you're at Les Houches, Argentiere or anywhere else in the valley. Naturally, being a low cost provider, for any extra bags there'll be a further charge.
Be sure to check their schedules. A local pick up service may be what's needed if you have an 8am flight from Geneva.