Job complete! For future reference:
To replace the wheel bearing hub assembly, remove the tire, remove the drum, remove the bearing cap and nut beneath. The bearing should slide off the spindle. If not, remove the brake shoes and use a pry bar behind the sprocket looking part of the hub to force it off. Reverse these steps to put the wheel bearing back together.
Total work time for me was about an hour.
Thanks for everyone's advice. This job was as simple as I thought, given the right tools. I needed to purchase a 36mm axle socket.