Mont Blanc literally means White Mountain.
Mont Blanc was first climbed by Jacques Balmat and Dr. Michel Paccard in 1786, and the next year by H.-B. de Saussure.
There is a regular airport transfer service from Geneva Airport to your accommodation in Les Houches, Chamonix & Argentiere operated by *Chamexpress  The price is 25€ per person, each way.
Ascension on foot
Although climbing Mont Blanc is not technically very difficult, the altitude requires proper training and equipment. Every year, several thousand people do it and several accidents are caused by improper preparation. A mountain guide is necessary unless you already know the place (660 € for one or two persons).
It can be done in July and August.
Usually done from Saint-Gervais-les-Bains with a night in the Goûter refuge.
Ascent by ski
Climbing Mont Blanc by ski is reserved for highly trained skiers. It's mostly glacier skiing. It can be done from March to June, depending on the snow coverage. A mountain guide is necessary unless you already know the place.
Usually done from Chamonix with a night in the Grands Mulets refuge.
Ascent by cable car
Climbing Mont Blanc can be traversed by a series of trams from the Italian side to the French side. It is a beautiful experience offering the comfort of heated stops with restaurants and the option of getting out to hike over the glaciers. Bring warm clothes. The return trip can be made by a bus which travels through a tunnel under the mountain.