From the Aig du Midi, cross Vallee Blanche. You can either follow under the southern side of Aig du Midi, then pass by the northern triangle of Mont Blanc du Tacul and continue for a short distance. Or take a more direct line across the vallee Blanche just remember this area is the start of the glacier zone (don't get into the "safe" vallee blanche frame of mined)
Once you get to the base of the face you will see many different options..
You can climb simply straight up the right hand side (of the rocks) in a direct line on easy snow up to approximately 55 degrees, late in the season there maybe a small rimaye but it should not cause you any problem. Grade F
Or you can move more to the left (heading up the middle) and work your way through mixed ground of snow and rock, it is possible to stay almost completely on snow till the last section by zig zaging the rocks, if you wish to avoid them. Grade PD to AD depending of the route taken.
Or You can go round to the far left hand side and climb up mainly over broken rocks (I have not climbed on this part so I can not real give a good out line) But from looking at it i would say approximately AD+ III / IV
Decent either down climb / rappel the way you came or walk off the ridge that runs to Mont Blanc du Tacul turn to Vallee Blanche at the Col (you can also go to the summit by this method, but it is very short and dare i say boring).
SEE THE ATTACHED PHOTO TO GET AN IDEA OF POSSIBLE LINE.
Really just depends on the route you take, but the further left you go the more gear you will need... so if you start with a rope, axe and crampons for the right hand side snow route and add a alpine style rack (a few medium sized cam's and a range of slings and a couple of medium to big nuts) you should have no problem in the other areas.
Don't forget the helmet.
I highly recommend doing one of these route before doing the Cosmiques route on Aig du Midi, both a quite short.. make a day of it and miss the morning rush on cosmiquies