This instructable may look long, but you could make it in a few hours.
I didn't feel like working in the workshop so I designed this so you don't have to use any power tools or hand tools that would make a mess.
Most of the items I had on hand. I just bought the lazy susan bearing ($2.19) and the tubes of silicone (~$7.00 each), and the binding post (~$1.00).
Using a Yarn Swift with the Ball Winder is a good idea. I made a swift out of wire hangers, a wine bottle, duct tape, and a box to stabilize the bottle. It is a modified version of the Yarn Swift at http://aemmeleia.wordpress.com/2007/09/05/diy-yarn-swift-desparate-measures/. I used 6 hangers instead of 4 and put the bottle in a box. Didn't cost anything!
Step 1: DEMONSTRATION VIDEO
The beginning shows the parts of the ball winder and yarn swift and the end shows how to use it. It might help as you go through the steps.