The best way to deal with bony fish is to poach them gently in broth and then flake out the meat, with can then be used in fish salads, fish cakes or soups.
Shad are especially bony, but northern pike, pickerel, carp, herring, squawfish, mooneye, buffalofish and many other fish are also born with extra sets of bones. Shad take the cake, though: They have 3,000 bones, but their meat is so tasty their Latin name is sapidissima -- "tastiest."
To get started, fillet the fish as you would any other, then skin them.
Now bring to a simmer some good fish broth; you will need at least a quart. If you do not have fish broth, use chicken broth. You could use water and wine, or any sort of a poaching liquid -- the point is to add flavor.