From the Col des Aiguilles Grises there is a short steeper mixed section to reach the Piton des Italiens at 4002m. From here there is a short section of a sensationally exposed snow ridge, though with any luck it may still be dark! It soon eases off, then easier slopes head towards the Dôme du Goûter, which you can traverse on its R side. Soon after this you join the main track coming from the Goûter hut near to the Col des Dômes.
Shortly above here is the Vallot Hut at 4362m, the highest building in France. It is an emergency shelter only that unfortunately gets abused and littered, but a quick visit to escape the wind is fine. From here on up is the Bosses ridge, leading to the summit. You pretty much follow it direct on the ridge, entirely on snow and ice, with a significant degree of exposure in places. There may be parallel tracks, useful as others will be descending. Surefootedness is needed and good crampon technique, as well as a short rope if you are safeguarding one or two other people of lesser experience. A slip is far more likely than a fall into a crevasse here, so a long rope is inappropriate and will annoy others, as it may appear like a trip line.
Slowly the whaleback crest angles off to your summit, which hopefully you will experience in the beautiful early morning light, the incredible view distracting you from the cold, and possibly your headache and tired body. The descent initially is down the same way, until the Col des Dômes. From here, unless you are extremely early, the best descent is to continue down the easy angled slopes and the major track to the Goûter hut. You could stay here if you have booked, or if not continue down the standard descent to the Tête Rousse Hut and hence to the Nid d’Aigle train station.