You can do the job with the wheel built -you don't have to take the spokes off of it like the bare hub in the video (it's not me in the video BTW.) He's just got a bare hub because it is easier to show what is going on without the rest of the wheel in the way but it doesn't matter. You can't do the job with the wheel in the bike

The "driver" is the long piece with the 4 prongs on one side and the 1/4" x 7 bearing cage in the other. The 1/4" wheel bearings are the only ones that are supposed to get grease. You don't want to let grease get out of the caged bearing area. Don't even get too much on the spring as it can slow it down and cause problems shifting into 3rd and hit neutral for an instant.

Sheldon's AW hub page sort of sucks. He talks about a lot of stuff that just confuses the issue. I've never had any issue with the "double-threaded" ball retainer or needing to mark it with a piece of yarn (WTF? how would this even work?) He also talks about not taking the spokes out since you can't take off the far face without the spokes/wheel built up. You don't need to ever take off the far end! If you do then you have serious problems -get a donor hub!

This is a handy reference with a nice exploded diagram of parts and nomenclature.