Start at the refuge du Couvercle and head North to the Talefre glacier. On the glacier (be aware of Crevasses!), continue North-West, passing the Aiguille du Moine on your left. Head for the first couloir on the right of the "breche Moine - Nonne". It takes you about 30 to 40 minutes for the approach.
It is not so easy to describe te actual route. It is possible to climb it slightly different every time.
Here is a try:
Start at the couloir right of the "breche Moine - Nonne" (later in the season, August, September the bergschrund can be quite airy) on the right hand side of the ridge. After 30m you will come on a platform. From there you'll need about 4 pitches to reach the main South-North ridge. These pitches are sometimes rather airy. Overall climbing grade III to IV (UIAA) From there you need to follow the ridge for some pitches to reach the "gendarmes" wich you need to climb to reach the summit. From the summit you rappel - climb down to the ridge again. Your now halfway the ridge and from here "le rasoir" or the rasorblad starts. This very sharp and beautiful ridge is about 100m long. Placing any slings or friends is difficult. This part is really unforgettable. After the rasorblade you'll have to climb (somtimes walk) down, following the "stonemen" to reach the "breche Nonne-eveque" from were you can climb or rappel down (stonefall!!). You'll reach the Talefre glacier easily. You'll need 4 to 5 hrs at least for the traverse. You'll reach the hut in about 20 minutes
Crampons and 1 ice axe for the approach and helmet!!! Stonefall is prominent at the Moine's East side.
The traverse: Double rope (2x 50m) slings, medium sized friends and stoppers, biners, about 8-10 draws, helmet!