Over the weekend I took Audrey's wheel apart. This is what the hub looked like at the start - pretty gross. The spokes snapped very easily so I was able to pull them all out of the wheel pretty easily.
As soon as they were all gone it was very easy to take the hub apart. These are all the parts. The balls sit in a rim just inside the hub and they are held in place by the bar and the shaped nuts. They are covered in grease which makes the bar able to turn around against the balls easily instead of rubbing off flat metal. I cleaned and rusted and treated the metal and it turn out like the next photo - pretty good improvement!
I took one of the old spokes to my local bike shop and was able to buy replacement ones. They come in 2 parts - they have a nipple (he he he) at the end that goes through the hub and they look like a screw at the top. Then there is a bit that looks like a long nut that goes in through the rim and connects onto the spoke. You can tighten it with a normal screwdriver and the idea is to keep the spoke from coming up though the screw cause it will puncture the tube.
I followed Sheldon Brown's instructions on how to respoke the wheel. It's a great article and really easy to follow. It's a lot easier than I thought. It's not completely true, as I obviously don't have a truing stand, but I got is as close as possible by looking at it spinning on the bike upsidedown. The spokes alternate at being on the right and left sides of the rim. If the rim is bending to the right, tighten a spoke on the left to pull it back. And hey presto - a shiny new wheel! When the rear wheel is ready I'll bring them both to the bike shop to be trued properly.