Ascension run

The Ascension Run is the final stage of the game. It begins by collecting the Book of the Dead and ends by ascending (or dying).

Rough phases

Enter and climb the Wizard of Yendor's tower via the portal in the correct Fake Wizard's Tower, OR, wake the Wizard with a mind flayer mind-blast or the sound of a drum of earthquake from outside his tower.
Retrieve the Book of the Dead from the wizard, by killing him or stealing it while polymorphed into a nymph.
Head down to the Vibrating Square.
Perform the Invocation on the Vibrating Square.
Retrieve the Amulet of Yendor from the High Priest of Moloch inside the Sanctum by killing him or sicking a covetous monster (like a powerful demon) on him.
Climb up the dungeon, fighting the Mysterious Force and the Wizard along the way.
Pass through the Elemental Planes.
Find the correct altar on the Astral Plane (that's probably the coaligned one, unless using a helm of opposite alignment or escaping in celestial disgrace) and offer the Amulet. But watch out for the Riders!
Go to #nethack on freenode.net to brag and collect your congratulations.