Nothing too hard. Takes quite a while, though - I can see why Klimmek wouldn't want to do this very much. Other than a few large predators and a troll, rather uneventful.
Right at the base of the last steps is the offering box. Even though I'm going inside, I leave their supplies there. I figure they have some sort of system, and I don't want to mess it up.
Once inside High Hrothgar proper, I'm greeted by the head Greybeard, Arngeir. He explains what in Oblivion is going on with the dragons and Shouts, and being the Dragonborn.
The masters take me outside to learn another Word, WULD ("whirlwind"). This creates a gust of air that pushes me forward at incredible speed.
After I learn this as easily as the others, Arngeir has a test of a different sort. I am to get the Horn of Jurgen Windcaller, the founder of the Greybeards and their Way of the Voice.
I came to Skyrim to learn magic. I suppose this is a practical exam.