After removing the wheel from the bike, I had to remove the gear from the hub. It's held in place by a snap ring, twist it off with a screwdriver:
Keep track of which order the pieces come apart. With the cog removed I unscrewed the bearing cone by hand, and removed these pieces:
This hub had 5 roller bearings arranged inside a large retaining piece. After unscrewing the lockring that holds the reaction arm to the other side of the hub, I was able to extract these remaining pieces:
Here is the nearly empty hub shell:
And here is how the inside pieces fit together:
I'm still not sure how everything works, since this isn't like a traditional screw type coaster brake. Regardless, I cleaned the parts up and started reassembling them with lots of grease. First I installed the pieces from the reaction arm side:
Next I replaced the roller bearings:
Then the ball bearings and the axle:
Now I slid the drive mechanism back into place:
And secured it with the bearing cone:
Now the cog can be reinstalled. I lined up the spacers in the order which they came off, then slid the cog into its 3 grooves and locked it in place with the snap ring:
Finally I reinstalled the reaction arm:
Done.