Steve,

The "stopper ball" is simply a little plastic ball with a hole in it. You run the dousing line through the spinnaker and before running it through the last attachment grommet (or ring) on the sail, run it through the stopper ball and tie a knot in the line...then attache the end to the sail. The stopper ball is a pretty common article (trying to attach picture). You can also use a Hobie-style trapeze stopper (the little black bow-tie looking thing) to accomplish the same thing.