The Rébuffat route is the original line that renowned climber Gaston Rébuffat and Maurice Baquet climbed on their first ascent of the prominent south face of the Aiguille du Midi (12,605ft/3,842m) on July 13th 1956. Today, this classic route is one of the most popular climbs in the region.
Here's an enjoyable video report of the climb.
Regular descent down the exposed Aiguille du Midi east ridge and down to the flats on the glacier on the south side of the Aiguille du Midi. Straight up to base of the wall from there. Watch for bergschrunds!
For the time being refer to the topo on the left and to guide books (see below). Note that route finding is a bit intricate in the upper sections.
Either rappel back down (plenty of anchors to pick from) or climb around the top of the pillar to the sightseeing platform behind it.
When rappeling, keep in mind that the route ascents the wall slightly diagonally to the left, so try to move slightly to the right to get back to the base of the route. Otherwise you may end up climbing snow in rock climbing shoes right next to large crevasse.