In reply to Matej:
Stay at Tete rouse, cross the grand coulouir before 10:00am (this detail is important, you will understand after you've been there) stay at the Gouter as well (ask on the door they may have space/cancellation) or discretely and I mean *discretely* bivvy but have no evidence of sleeping/bivvying during daylight. Depending on weather... 02:30 breakfast and be packed up and walking 03:00 for summit you want to be early as crowd management on the Bosse ridge is a big problem so early again is your friend, 03:00 start isn't actually as early as it sounds and others will be ahead of you (good as you can follow the line of head torches)
Oh and make sure you can walk in crampons without tripping or ripping your ankles. Ice axe arrest essential and learn to move together on a rope.
I recommend descending down the Grands mulet route not back down the way you came, it's a nicer walk down better views less crowded. There may be some *hopefully* obvious crevasse so make sure you are roped. Again lots of other people so route finding is largely follow the crowds (obviously have the skills to do everything if you were the only people on the mountain, in case of weather). In bad weather descending Gouter may be best emergency route off
enjoy!!